Jump

Before the word Verticality became the new buzzword in gaming, the jump was the essence of that idea in it's most basic.  For either exploratory or combat purposes, the ability to move upward in a game produces a whole new dimension in gameplay.  Without the jump, platformers would not exist as they do today, and combat would never know these spectacular combos we use to smash enemies to the ground.  It comes in many shapes and forms, but the only constant is that it's what gives games depth.

Exploratory
Jumping for exploratory reasons in games gives developers means to create soaring levels in games such as Super Mario Bros. and Metroid, rather then simple side scrollers.  The freedom it gives for level design has allowed for environments in the air, were the player will have to jump from one platform to another, and more dangerous, challenging environments with pits and chasms to cross.  It allows for far more creativity in the form of secrets and hidden items, in that something above or below the screen will make it harder to find. It creates more challenging puzzle solving tasks, with clues and pieces of a problem now involving objects in the air, gravity, and creating height to jump up to a goal.  

Combat  
Jumping in combat has created a whole new dimension in fighting.  From Mario onward, attacking enemies in the air such as in Ninja Gaiden, has always been one of the most satisfying ways to finish off foes.  From creating thousands of new types of moves and combos to dodging enemy attacks, the jump has given the player a better tool in combat than "Duck!".  In old school side scrollers such as Metroid, Samus ability to jump meant enemies could also be found in the air as on the ground, so using leg power and the environment to get right up there with them was always good fun.  In fighting arcade games such as Street Fighter, the attack from the air created some of the most surprising and powerful combos, along with a new way to dodge attacks, making the back and forth attack and evade pattern that much more interesting.  In newer action games such as Ninja Gaiden, Ryu's attacks in the air are some of his most deadly and slick looking moves, and evading enemy attacks by jumping is crucial to success in most boss fights.  

Types of Jumps 
There are so many varieties of jumps in video games, many of which are franchise specific, that they are too numerous to list here. These are some of the most common or well known jumps.

• Jump: Up, forward, back, classic and still relevant to this day.
• Double Jump: The curious ability to jump once, then again in midair to create more height.  Some games even have triple jumps, but it's rare enough that it doesn't deserve it's own point.
• Flip: Encompassing front, back, and side flips, this cool looking jump makes many a deadly combo in combat as well a dizzingly stylish way to get from A to B.
• Wall jump:  Jumping towards a wall, and jumping again off said wall is seen in games like Mario and Ninja Gaiden (Flying Bird Flip, anyone?) also includes wall run jumps, etc.
• Long jump: In some games, getting the characters to sprint before clearing a chasm will result in an extra long, arm flailing leap.
• Assisted Jump:  Using another player, in coop or single player, to give an extra boost when jumping. 
• Environment Assisted Jumps: Uses forces such as vents or trampolines or big buttons (Sonic the Hedgehog) to blast off.
• Rocket Jump: There are games out there (Rocketman!) where the character uses a jetpack device to assist in making large jumps.
• Force Jump: Only applies to Star Wars games, but oh well.  Uses the power of the force to create higher, longer jumps.