personally I use
http://www.soundsnap.com but now they charge money for the sounds. Still it's a great library of sounds and you can listen to every one before buying anything. Take a look

Also if you're serious about game making you should either get account like that, buy a package of sounds or buy a good hardware for sound recording.
If it's only hobby or indie stuff then I guess you just have to google everything and hunt for the sounds you need

Good place to start is to browse through the public domain SFX pages like:
http://www.pdsounds.org http://www.freesfx.co.ukhttp://www.freesound.org/