Depends on your language.
I have used NetBeans for Java games (which is free) and Visual Studio (which has a free 'Express' version) for C++/C# games.
If you are making an XNA game then I belive you need Visual Studio 2008 (at least there was no support for 2010 in June when I was using it), especially if you want to stream it to your xBox 360 to test.
What are XNA games? Kinda heard about them. Which Eclipse? I'm overwhelmed by the choice :S Any GUI choices to started with as well? What languages would I need to learn? I'm learning C++ with my friend, when I have time. I'm happy to learn anything else I need - Even dead languages.
The PM was more of a private thank you than an ask for help tbh.
To get started programming in XNA I sugest you learn some C# first and make a few simple applications or command line text-only games like blackjack or hangman etc. Then join the Mircosoft XNA creators club at http://creators.xna.com where there are plenty of tutorials and sample code to help you get started.
A reasonable knowledge of C / C++ is a must when programming with openGL. See the Neon Helium (NeHe) lessons / tutorials at http://nehe.gamedev.net/ I used them when I started learning openGL, and still do from time to time tbh :)
I just posted this to someone else but I'll show it to you as well:
A Java PACMAN game tutorial, I have no idea if it is any good or not as I am actually at work atm and dont really have the time (although I do seem to find the time to come on here lol)
Anyway, I digress, here is the link. http://www.angelfire.com/games4/anirak/tutorial/day0/