Also, if you modify an existing image, sound or music file, is it now your work?
In the US....
If you have modified an existing image, sound or music file (or any other copyrighted work), you have created what is known as a derivative work. I.e. a work that is derived from an existing work. (http://www.copyright.gov/circs/circ14.pdf)
The right to create a derivative work belongs to the owner of the original work. It is not legal to modify someone else's work without explicit permission. (there are a limited number of exemptions to this, but none would fall under videogame use). So if you have a sound effect, alter it, and then use it in your game, you are in violation of the copyright of the original sound, even if it is unrecognizable from the original, since your sound is derived from the original sound.
What if you completely replicate it from scratch?
That depends on what it is...
If you "completely replicate from scratch" a song, then you are in violation of the copyright of the song itself, even though you are not making any use of the recording of the music. (there is a possible exception, but it doesn't apply here).
if you "completely replicate" a sound effect 100% from scratch--that is, you use your own original recordings or synthesizers and replicate something that sounds like the original sound effect, you actually are generally NOT in violation of any copyright. It is important that you are NOT using any pre-existing .wav files-- you need to create your own.
If you 'completely replicate' the art from an image --i.e. say you were to open up CorrelDraw and replicate Andy Warhol's famous "Campbell's soup can" by free-hand drawing, then you are in violation-- you have made a derivative work (of Warhol's work)
Ownership of a derivative work is a bit tricky. Technically, if you alter a work, then you own only the changes that were made, but not any of the underlying copyrighted material. So say you were to create a US flag out of little red, white or blue Mario's (Nintendo's mario). That is a derivative work, since it is derived from the copyrighted image of Mario (the US flag is an image in the public domain). But the "use of marios to make a flag" belongs to you (not Nintendo). But in any case, you can not reproduce your flag because you don't own the copyright to Mario's image. In fact, simply by making your Mario flag, you have violated Nintendo's copyright. But neither can Nintendo then go sell your flag design. EDIT: For clarity-- in the example above, you would not own a generic "make a US flag out of Marios" copyright. You would own copyright to your specific expression of the US flags made out of Marios. Nintendo would be perfectly within their rights to make their own Mario flag, as long as it wasn't identical to yours.
In general, if you are only doing something for yourself, for your own education, you probably don't have to worry about this. But if you are going to put your game out into the market in any way, you need to make sure you have proper licenses for any and all content on which your game is made. Music, sound, art, code, etc...
Brian Schmidt
GameSoundCon
p.s. As a brief aside... there is no question that it is not legal to make and distribute an unauthorized derivative work. But sometimes it works out... The creators of "Red vs Blue" (machinima based on Halo characters) was a pretty clear non-authorized derivative work. But rather than force them to shut down, Microsoft said "hey, this is way cool..." and engaged the makers of Red vs Blue, even including their work for Xbox download, etc.. I'm not advocating the creation of unauthorized works--just reporting an interesting story 
