Finding a game engine is quite easy. You just use Google. But if you insist....
Reality Factory(
www.realityfactory.info) - my first experience in game development. Create 3D FPS games easily, you can create other genres but it's harder to do.
Unity3D(
www.unity3d.com) - This is more complicated to learn than RF. Jediaction can help you and I can help a little, I'm still sorta new to unity3d and am definately still learning ;D
XtremeWorlds - If you're interested in making MMORPG games, XtremeWorlds is a free (2d) MMORPG maker that will help you create MMO games easily. Plus there's a scripting language that let's you add custom features.
Eclipse - This is a bit better than XW, but is less stable and has no scripting, you'll have to program you're custom features with Visual Basic 6
Genesis2D - Pretty much an advanced version of Eclipse. It's the best engine out there when it comes to features but it's very processor heavy when it comes to server hosting, you need a powerful computer to do.
3D Game Engines (Pros and Cons)
Reality Factory
Pros:
Easy to use and distribute games
Cons:
Not as powerful as other engines
Minimal Community Forums (though I'm still there

)
Unity3D
Pros:
Powerful
Active Community
Mac and Windows Support
Pro Version (cost money) includes PS3, Xbox 360, Wii, iPod, and Android support
Cons:
Hard to use
Hard to master
MMORPG Engines (Pros and Cons)
XtremeWorlds
Pros:
Scripting Language
Activeish Community
Cons:
Not as Powerful
Eclipse
Pros:
More Powerful than XW
Open Source
Cons:
Doesn't Start With Questing
Genesis2D
Pros:
Lot's of Good Features
Cons:
Hard To Understand
Processor Heavy (needs powerful computer to host server)
I recommend unity3d. anyways have fun!