Was gonna suggest Freesound, but it's already been suggested... there's also audio sections at OpenGameArt.org, which could be a place to look for music (there's some really good composers there, like Alexandr Zhelanov, but there's almost no quality control so be prepared for digging a bit to find the true gems). BFXR is pretty good, the main caveat is that it only does retro sounds (which can sound really out of place in games that aren't retro)
Make sure to
note down licenses of everything you get, preferably in the filename you save stuff under. Saves lots of time later. And you might as well veto stuff before you download it, so that you don't base your entire soundscape on non-commercial licensed stuff when you plan to make a free game, and then have to replace the entire mood if you decide to go commercial later.
I'd also recommend getting used to at least Audacity for editing sounds, stuff like paulstretching and frequency-domain editing can do a lot for the overall quality of a sample. Also remember that you can make a truly unique sound by overlaying several sounds, as demonstrated in this GDC talk: