In the Store page of every Steam Game you can check if one of these symbols is available. or Usually in all recent games (2-3 years), if a controller is enabled, there are high possibility that Microsoft Xbox 360 works and is well supported.
But to be sure I always suggest to take a look to that game specific forum.
Most of times there are users that already asked for Xbox 360 compatibility.
gaming.stackexchange.com/users/730/Drake
An xbox controller can be used on a PC, but it really depends on the game whether it's supported or not.
Unfortunally, Bioshock 2 does not support it.
See here :
I talked to the dev team about controller support for BioShock 2, and I want to let you know that we won’t be adding this into the game in a patch.
The decision not to support the controller was not made lightly, and to add it now
would take a complete re-envisioning of the UI that the team worked so hard to create.
I’m sorry for those of you who are disappointed, and I want you to know that your comments and concerns have been heard and will be taken in to account when we are planning in the future.
gaming.stackexchange.com/users/14/juan
You can use ANY controller that works on a PC to play ANY game you want.
Just get yourself a key mapping program.
Xbox 360 controller, PS3 dualshock, any 3rd party gamepad, etc.
If your computer recognizes input from it, you can use it in games.
I do it all the time
bc
I'm disabled and not physically able to use a mouse and keyboard at the same time.
There are a couple of decent keymappers out there, but imo the best by FAR is Xpadder:
http://xpadder.com/ which uses an intuitive GUI to walk you through setting up the controller to mimic any combination of keys
\ mouse that you like.
It's a shareware prog that costs $10, but it's worth every penny.
It'll let you create complicated macros that include mouse movements, clicks, wait periods, key presses, holding down keys, etc.
-- and then assign that macro to a single button on the controller.
You can even assign different macros depending on how far you tilt the stick on your controller.
For example, you can set it up so that tilting the controller's left stick to less than 50% of its total range will mimic "move the mouse forwards while holding down Shift and then press the R key," but tilting the same stick to more than 50% of its range will be the same as "click the left mouse button, wait two seconds, then quickly press the Y key three times in a row".
In short, you can make the controller do anything that can BE done with a mouse and keyboard, and it includes support for "rumble" and for multiple controllers at the same time (for multiplayer games).
You can even have it so that a single button or stick on the controller will mimic up to 10 different key\mouse actions, so that you're not limited by the number of buttons on the controller, because it's possible to set a button to shift the whole controller over to config #2 where config #2 is an entirely different set of key\mouse combos for each button.
And no, I'm not affiliated with Xpadder in any way...
just a gamer who is incredibly thankful this program exists so that I'm able to enjoy PC games that would otherwise be off limits for someone with my limitations.
gaming.stackexchange.com/users/19529/chaospearl
There is no correlation between Steam and the ability to play with an Xbox 360 controller.
This is depending on the game you want to play only.
Usually, if a game is available for both PC and XBox 360, it will accept the controller.
But again, no guarantee.
gaming.stackexchange.com/users/69/Gnoupi
Some games are listed on their product page as supporting controllers.
For most modern games, this includes the Xbox 360 controller.
For games that don't, you can use controller mapping software to translate your controller to keyboard/mouse commands.
For example: http://pinnaclegameprofiler.com/
gaming.stackexchange.com/users/108/Whatsit
On the Steam store it will actually tell you whether or not the game will be compatible
gaming.stackexchange.com/users/873/user873
For games that support the Xbox 360 controller (which is certainly not all of them -- and Bioshock 2
I believe does not), you can simply plug a wired Xbox 360 controller in via a USB port.
gaming.stackexchange.com/users/875/Xemu
Depends on the game.
For example, I have set up Borderlands, Defense Grid and Half-Life 2 (and TF2/L4D) to work with my 360 controller.
It depends on the game and its support for gamepads.
gaming.stackexchange.com/users/None/
I used a Wired XBOX 360 Controller and it wouldnt work, but yes some games do support it
but Bioshock is not one of them
gaming.stackexchange.com/users/9941/KalebT44
I bought  BioShock 2  on Steam in the sale a couple of weeks ago, but I'm better at playing FPSs with an Xbox 360 controller than with mouse and keyboard.  Is there any way for me to use an Xbox 360 controller to play Steam games?
How can I use an Xbox 360 controller to play Steam games?
gaming.stackexchange.com
<steam><controllers><bioshock-2>
gaming.stackexchange.com/questions/2178
gaming.stackexchange.com/users/858/Chris Salij
On the Steam store it will tell you if the game is compatible. An xbox controller can be used on a PC, but it depends on the game. You'll need to get yourself a key mapping program. It seems to depend on the game, checking the game forums may help, and that particular game may not support it. Other alternatives are key mapping programs.
Users say that it depends on the game. Negative reply to say that that particular game does not support it. Running a key mapping program is suggested. A user suggest looking at the game forums.