Kerbal Space Program is a great game, but it is poorly documented. I am always on the lookout for obscure features, and I found an excellent list online that can be used to start a list here. I've deleted a few that aren't true of the latest version and added a couple. Add more to the list if you have any!

Building craft

• Shift-clicking any part of the ship will select the entire ship for movement, while Alt-clicking copies that particular part and everything attached to it.
• Holding shift while moving the mouse wheel zooms you view in and out, rather than moving up and down.
• Ctrl-Z can undo the last change you made to your craft, though be aware: it often undoes the 2 most recent changes. Ctrl-Y reverts the undo process.
• You can turn parts 90 degrees with QWEASD, and make precise adjustments with Shift-QWEASD: this turn the part 5 degrees, so press shift-[direction] 9 times to rotate the part 45 degrees in that direction. Note: this will never go the direction you want it to go first time. Accept this and be at peace.
• If a part has become turned and twisted in a way you don't want, hitting the Spacebar while you have it selected will return it to default orientation.
• X increases build symmetry number, and shift-X decreases it - C and Shift-C quickly toggle angle snap.
• The action group menu lets you add all kinds of functionality to the buttons 0-9, to the 'abort' button (typically bound to Delete or Backspace), to the lights button, to the landing-gear button, etc. Click on a the action group you want to add something to, then click on the part, and the menu will show all the part's functionality which you could use. This is useful for grouping all your 'science-collection' to one button, or for single button extend/retract all of your solar panels, or maybe you would like your Ladders to extend too when you press G for your landing gear.
• If you're building something that you wish to use in a sub-assembly (like a lander or satellite which you want to attach to a different rocket) start with a docking port, not the craft's main command capsule or probe core! This allows you to select everything from that point on which makes up the actual craft and save it as an assembly without getting stuck with the root part - alternatively, save an entire craft as a sub-assembly by shift-clicking any part of the ship to select it all, and save that.
• You can tweak the amount of fuel in fuel tanks at launch while building, as well as extend/retract landing struts and turn lamps on and off by using the right-click menu.
• Solid-fuel boosters can be throttled with the thrust limiter using the right-click menu to adjust the burn time and thrust-to-weight ratio.

General

• The F5 button quicksaves the game! So long as you are not about to crash, your thrust is set to 0, and you are not in atmosphere (unless you've landed), you can create a savepoint. Later, holding F9 will return you to this save. WARNING: incautious loading if you haven't saved for a while can wipe out hours of work!
• Additionally, pressing Alt-F5 will allow you to save the game with a name, and Alt-F9 will allow you to choose a quicksave to load.
• Physics-warp works while engines are throttled up! If you're using ion engines with an hour-long burn time, or if you're flying a stable plane in atmosphere, or even if you're just walking with an EVA Kerbal you can hit Alt-. to increase time acceleration to X2, X3 and X4 even while thrust is engaged. Bonus: this may make your physics act in hilarious ways, like squishing your rocket and making your Kerbal dance.
• You can move fuel (and other resources) between different tanks by Alt-Rightclicking on each of the two tanks you want to transfer between, and pressing 'in' or 'out'. Press 'stop' when you're done.
• You can pan the camera position relative to your craft by holding the middle mouse button, this is great for screenshot composition - re-center it afterward by double-clicking the middle button.
• Science can be retrieved from science modules like goo canisters by approaching them with an EVA Kerbal - this science can be stored in any command pod so that it becomes unnecessary to bring each of your science modules down for a landing.
• Bring up the Navball in map-mode by clicking the little arrow tab at the bottom of the screen or press the Decimal [ . ] key on your keypad.
• Hit Alt-F12 to bring up the debug menu. Here, you can see and modify much of the internal data the game uses.
• Use Alt-scrollwheel to change the FOV.

Flying craft in space

• Alt-L will lock your staging: avoid accidental decoupling.
• When planning maneuver nodes to intercept distant bodies you can click on the periapsis/apoapsis indicators to display these numbers permanently, rather than having to hover your mouse over them. Click cautiously to avoid clicking on the orbital path itself, as that prompts a maneuver node.
• Caps Lock will turn on 'precision' controls, which decreases the sensitivity of your directional and RCS maneuver input. Note: this will also effect the functioning of your SAS, possibly reducing its effectiveness for certain maneuvering.
• When adjusting the thrust axes of a maneuver node, use the scroll wheel while the mouse is over a symbol for very fine adjustments. Scrolling up increases the thrust, and scrolling down decreases it.
• Holding F will temporarily turn off SAS if it is on. This is useful to let your craft spin to a new position before letting SAS hold it at wherever orientation it has reached when you release F. Alternatively, it will temporarily engage the SAS if it is inactive: this can be used to arrest a spin without draining power from your batteries with constant-on SAS.
• You don't need to switch to Translation-mode to use your RCS to maneuver for docking: the IJKL keys will do that in normal staging mode, and H and N thrust forward and reverse with your RCS respectively - even from the map view, so long as you have the Navball up (which is also required to change your thrust settings). This can be extremely useful for fine-tuning at a maneuver node to optimize a distant intercept point.
• Having trouble orienting your craft for docking? Rightclick on the exact docking-port you're aiming for and select that as the target, rather than the entire ship. Also, right-click on your own docking port and select 'control from here' to have your navball display your vectors and target position relative to that part of your ship.
• Also for docking, you can point one ship to orbit normal orientation, and the other to orbit antinormal. These directions remain the same for the entire orbit.
• Activating time acceleration arrests your crafts rotation! This can be very useful if your craft has too little torque to come to a stop easily - I consider this to be cheating somewhat, but it is what it is.
• Pressing Tab moves your view centering in Map mode, cycling through different celestial bodies - useful for far-away maneuver nodes and encounters. Backspace returns the view to your craft (in Map mode).

Flying in atmosphere

• If your (space)plane is veering slightly in one direction, you can hit Alt-[direction] to adjust the 'trim' of your craft. This moves the standard position of the control surfaces slightly in that direction to let you find a stable point. Alt-X will reset this trim.
• Jet engines are finicky - they increase thrust up slowly and when you cut throttle they don't shut down instantly. However, you can still have precise control by binding your air-intakes to a hotkey when you build: hitting that hotkey will immediately starve the engines of oxygen, instantly cutting all thrust from the jets (exceedingly useful for VTOL control and landing) - a similar effect can be achieved by directly binding the engines to a hotkey.
• When you're coming in for a landing and need to quickly slow down you can hold B to use your landing gear to brake, or alternatively click the 'brake' icon to the right of your altimeter to permanently engage the breaks on all your wheels, freeing up your fingers for precise maneuvering on landing. It's advisable to disable the breaks on your front wheel(s) to avoid flipping the craft over forward!

EVA

• Kerbals have headlamps! Hit L while on EVA to turn on your Kerbal's helmet-mounted torch.
• Kerbals can run! When walking on a surface, hold Shift to see your Kerbals waddling faster. Note: this does not work while your jetpack controls are out!
• Shift-Space will make a Kerbal jump back from a ladder instead of releasing it and dropping down - Shift-WASD-Space will cause them to jump up, down, left or right!
• Engineers can repair damaged rover wheels (and a few other damaged components) when standing nearby and using the right-click menu
• Sent out a probe that died due to lack of power because you forgot to deploy solar panels? EVA Kerbals can manually open them! Again, this is through the right-click menu.

Building, Part Tricks

• Small gear bays are immune to physics and despite their default configuration they can steer. i.e. that 0.5 ton mass? doesn't make your craft heavier. Drag? Not from landing gear. Activate steering in their right-click menu.
• Struts and fuel lines also have no physics, as well as having no clipping (debris can fly right through a strut without it doing anything to it).
• You can use Cubic Octagonal Struts to connect anything to anything else in any orientation. Place 8x symmetry octagonal struts with 48-7S engines beneath the outer edge of an orange tank under a probe core, with another 6x symmetry set inside that, and you don't just have an SSTO, you have SSTMO: single-stage-to-munar-orbit.

Oh jeez, there are a ton of little details here I had no idea about. Cheers!

I started playing avidly quite recently, definitely had several "aha!" moments while reading through this. Thanks very much!

This is incredibly helpful. Thanks, dude!

Added a couple more, including this discovery while watching a Scott Manley video:

• When adjusting the thrust axes of a maneuver node, use the scroll wheel while the mouse is over a symbol for very fine adjustments. Scrolling up increases the thrust, and scrolling down decreases it.

There are still hidden features to find!

Bookmarking this thread!

Kerbals collecting science is awesome. I had no idea of this. Thanks for this thread!

If this list would contain a "Must-have Mods" segment as well, then it would be perfect... I love KSP, but I've never modded it..

I am one of those weirdos who believes in playing as much as possible without mods, but even then the interface is bad enough there are a few easy recommendations to pick up once one has gotten used to the basic idea of rocketry.

Data Extensions

• Kerbal Engineer Redux (Latest version is still only on their Github) - Gives extended orbit and physical location information. Also gives important build and mission planning info in the form of deltaV and thrust-weight-ratio calculations which are invaluable in determining where your rocket can go and tuning handling.
• MechJeb - All the same info as KER, but also with a suite of auto-pilots. The auto-pilot isn't the necessary part, but I assume you are an adult who knows if you'd rather twiddle your own sticks or try and make a robot not fail at its job.
• Keep in mind for the future: RCS Build Aid - You may not be docking or making VTOL aircraft or rover rocket cranes for the near future. But when you do, RCS build aid gives you all the information you need about torque to understand if your space station shuttle can smoothly translate itself during docking maneuvers, or if your VTOL or rocket crane is going to cartwheel comically around.

Interface Extensions

• Kerbal Alarm Clock - Not necessary by any means because even in campaign there is very little time pressure when the average contract gives you a decade or more to do something. But if you like playing the itinerant mission controller having a dozen missions going at once, KAC is invaluable for setting up reminders for when you need to burn or when you are approaching atmosphere, or any other reason you'd like to jump in the seat of an active mission.
• Precise Node - Lets you enter node parameters as numbers, as well as step parameters by button. Optional detailed info view gives you info on the result of your burn such as orbital parameters and even escape trajectory parameters.

Bonus tips

• Efficiently going to other planets is a matter of geometry - Duna is relatively close to Minmus from an energy point of view, if you know the correct time to go. A basic tutorial on the general guidelines for planning trips yourself by hand is here. A full featured window calculator and ejection parameter calculator is here, with bonus porkchop plots that let you select inefficient but faster or convenient routes.
• Watched the YouTube tutorials and now think you have a general idea of rendezvous and docking? Check out this Imgur album for summarized details of different rendezvous techniques and a quick reference on how Navball icons work once you are approaching a rendezvous.

I second the recommendation for Kerbal Engineer.

Another one that makes space probes more useful: SCANsat. Here's a video describing its use.

And a mod that makes early science gathering in career mode easier: Sounding Rockets. It even includes a stick to hold the rocket in place for launch!

Wondering if I could get some tips for the Science Career mode. I have literally just started playing the game and I'm banging my head against the controls of flight. So far I'm not enjoying trying to evade spinning and such and while it isn't going to cause me to stop, I wish I could just by pass this part or at least make the controls easier and less prone to infinite spinning and eventually explosions. Also just some general tips on how to approach the science aspect. Guess I'm just trying to learn what my limitations should be with only a few upgrades already. I could easily strap 10 rockets together and get out of space, but should I be shooting for the moon right now?

@nightriff: As far as goals, my progression through the career (the science + contracts one) started off by first getting a ship to launch up and down without losing stability. I then focused on stabilizing in-atmosphere flight with rockets so I could do a bunch of contracts. Then my goal was getting a stable orbit around Kerbin followed by fly-bys of the Mun. That's where I'm at right now (I'm taking my time with that game).

As far as stability tips, that depends on what your problem is. Keep the weight centered and remember that fuel drains from top down, so that dynamically affects your center of mass through flight. If it's lower than center, the top of the craft creates a lot of drag. That drag is a force that treats the CoM as a fulcram and flips the rocket backwards (which just causes it to continuously rotate as it tries to stabilize). To prevent this, you put winglets and/or fins on the bottom of the rocket which, when the rocket starts to flips, create more drag than the front of the rocket, and realign it correctly. The faster you travel in atmosphere, the more force the atmosphere will push on the front of that rocket through drag. Try and keep your rockets maximum in-atmosphere speed around 500m/s. You can help control this during booster stages by right clicking the boosters during contruction and telling them at what 100% you want them to burn. 50% means they'll last twice as long and produce leas force on the rocket.

Hope all this helps!