My aim is to be able to create sound effect for a game: gunshots, laserbeams, explosions, roars etc. I know of "sample collections" like the General and I like them, however I'd like to have some software "sound generators" that give me _complete_ freedom over the end result. I've tried a variety of sound software- FlStudio, Cubase, Reason etc. but they seem geared more versus making music. So: what do you recommend for game-type sounds? What soft synths? Or programs? What is the best in your opinion?

Sound Forge

Access SF's synthesis engine and take it from there.

Try Audacity

Try the awesome sfxr:home page and blog post with with several ports linked from comments

A couple videos I made which may or may not be helpful showing how to make some rudimentary sound effects with audacity (laser guns, explosions, gunshots).

Not the best, but maybe better than nothing:

laser sounds
explosion sounds