Obligatory Specs:
i5-3570 3.40 GHz
Geforce GTX 650 Ti 1GB
2TB HDD
16 GB DDR3 RAM
ASUS P8Z77-V MB
Windows 7 64Bit

I fully expect to get no solution out of this, my own internet searches have confirmed that I am the only human being to have ever had this problem.
Got this PC custom made a bit more than a year ago, and for the most part, it operates swimmingly. Considering an upgrade to the GTX 660 Ti, but that will wait until prices go down a bit more.
However, in certain games, framerates are obviously choppy for no real reason whatsoever (sorry, but I don't collect FPS data for all my games, I could run benchmarks if someone wants me to. When I say the FPS is noticeably bad, just trust me on this). Most of these games, I've noticed, either have DX 11 as an option or just run on DX11. Just as random examples, four of these games are Bioshock Infinite, AC 3 and 4, and FarCry 3.
The FPS in Bioshock Infinite just constantly remains choppy, no matter how much I tweak with the settings (I know that Youtube videos aren't the best place to get information on how my card should perform, but I should at least be able to get a stable FPS). Additionally, Elizabeth herself in Bioshock Infinite suffers from a LOT of physics glitches/bugs. Her hair and dress just go nuts for no particular reason.
AC 3 wasn't much better. Terrible framerates (even in the menus, when there is no 3D rendering going on), the robes on the main character would freak out and graphical glitches abound, especially in the ship at the start of the game.
AC 4 didn't have the graphical glitches, but it does have a constant choppy FPS.
FarCry 3 is interesting, because enabling DX11 on it slows EVERYTHING down to a crawl, including the company logo intro screen and the main menu (again, where is no 3D rendering going on). Switching to DX9 however, and I can just bring all the settings to the max and have an excellent, playable FPS.
Just in comparison, the same video card runs BF3 with no problems whatsoever, and recently ran Outlast just fine at full settings (I know Outlast isn't a graphical powerhouse, but it wasn't a simple looking game either).
The glitches in Bioshock Infinite and AC 3, and the slow running menus in FarCry 3 make me think that there is some basic flaw going on somewhere, but that's just conjecture on my part.
So guys, what the hell is going on?

The 650 TI isn't the greatest video card in the world. I'd expect it to have issues with some of those games. I have a 770, and I wasn't happy at all with my AC4 framerate until I did a lot of finagling. The graphical glitches sound odd, and I can't really speak to those, but I think you're generally expecting too much from your hardware.

Have you checked your GPU temperatures while running DX11 vs. DX9?

And don't get a 660 ti. A 760 is less expensive now for some reason (mainly because I have a 660 ti, and Nvidia hates me.)

What settings are you trying to run games on?

Make sure that SSAO, PhysX, and tessellation are all off (I don't know if all of those games support PhysX). A 650 ti isn't an especially powerful video card. It can get the job done, but not always at max settings. And PhysX is an Nvidia thing, but it still takes a toll on their lower cards.

PhysX takes a toll on all cards. I'm running a 780 and I still need to turn PhysX off if I want to keep my graphics settings on max at 1080p/60fps.

@jjweatherman: I can't even get Assassin's Creed Liberation HD running on my GTX 760 smoothly, just spent £400 on a new PC that won't run a vita game.

Honestly, I'd be happy accepting that I should get a new card if it wasn't for those glitches and the extreme slow down in menus. Because of those, I just have this nagging doubt that I could just need a software fix somewhere.

The one thing you didn't mention is what drivers you're using...I know it's such a basic thing, but you never know.

It sort of sounds like the games frame rates might be fluctuating like crazy for you. If you have a game that fluctuates from 60-30 its going to look really damn choppy even if 30 and 60 are both by themselves acceptable frame rates.

332.21, thanks for the reminder.

I wish. In my local AUS stores, its about $350 for a 760, and $300 for a GTX660Ti. Also, because of the power requirements of the 760, I'm a bit hesitant about using it with my 550W PSU.

It definitely sounds like your Graphics Card is running out of memory. I remember watching a video about 1 GB video cards and how awful they are for gaming now. I mean, it is only 1 GB of GDDR5 and most games tend to use 2 GB nowadays.

Here is an article I found explaining a little more about these cards. I would suggest that you try bumping down the resolution and turning off AA.

To be fair every asset in that game has been reworked and it's running inside the AC4 build of the Anvil engine. That being said there's no reason why a 760 couldn't run it fine with the AA turned down (the top 2 are TXAA flavours).

That machine is unbalanced as hell.

The most expensive part in a gaming rig should be the graphics card.
You've spent twice as much on your cpu as you have the graphics card.

Even your ram might have been more expensive than this most crucial of components.

Well, as it is right now, you have a great foundation to dump in pretty much any single gpu solution into, without worring about bottlenecks, because you have such "over-dimensioned" components in your build at the moment.

If you want to see what a 650 ti is supposed to perform like, take a look at the game benchmarks here.

If you have a proper 550W PSU, you could run a 780 Ti on it, and pretty much everything on the AMD camp as well.
A 760 Peaks around 170 watts.

PSU recommendations have to take into account every other component a user might have in their system, as well as the fact that people buy wood psu's for 30 bucks just cause they claim to be capable of delivering 1000 watts.

Personally, i hate buying two graphics cards from the same series, Kepler has been around since march of 2012, i think.
If you feel like it, wait for Maxwell, which in this time-frame, is just around the corner.

@devildoll:

Thank you for telling me this so much. I honestly had a fear that if I upgrade my graphics card my other components will start becoming bottlenecks. Guess I have a ways to go with building PCs =/.

I agree with WasabiCurry

You have a video ram bottleneck. Unfortunately 1GB is not enough to run some of the newest games at 1080p. I would recommend running the lowest anti-aliasing setting you can stand. If you want to turn it off just to see if you get a performance boost, try that. Like a lot of other people have said, Physx consumes a lot of frames too. But I honestly think a lack of video ram is your main issue here. Texture quality consumes a high number of frames as well. But the day I have to turn the textures down from ultra is the day I curl up and weep.

@devildoll: What he said. 550 Watts should be enough for almost any single card. Something like a Nvidia 780 Ti or an R9 290x might be too much, but short of that your PSU should be fine. Your CPU and RAM is also plenty.

Far Cry 3 is also pretty demanding. I can max out most games or close to it, but Far Cry 3 has to sit around medium to play well.

without a doubt the GTX 650 ti is weak as hell to play a game like Far Cry 3 on max... consider dramaticlly upgrading that... especially for the newer games you will more than certainly need more power in the GPU department, you wont even rival the new consoles with that. 550WATT is low but sufficient so long as your not overclocking or anything but to be fair, 500watt you really really pushing the PSU, and if you have a poor quality PSU then that is defintely going to cause you issues, when GPU manufactures suggest a PSU WATT, thats of the higher branded 550WATT, not a regular PSU but for what the OP has, is fine for a GTX 650 TI. You also have to consider how many CPU cores you have as well, which use more PSU of course.

I had similar issues with a GTX 580, games would feel choppy and "microstutter" even though it's a single GPU and the framerate counter remained 60 fps, as well as some intermittent stutters/freezes, then bought a new AMD card few months ago and no more issues. It turns out it's to do with Nvidia drivers, which is kinda funny since everybody kept telling me that Nvidia had better drivers than AMD, yet in my experience it was the opposite.

This is my experience though, you might not get the same result.