Oh man, I have way way way too many favourite tracks! Choosing only 1 for each category is too hard. Argggh....
So I'll just list a whole bunch of stuff which I truly love for life and can't let go off:
dimension 2012 by necros, featured in crusader: no remorse, level 01. if you think there's some better video game music, i think you are wrong. it's as simple as that.
stars.mid, sod map31 by forty-two. i'm fairly certain i haven't heard anything better in the midi genre.
These aren't representative of my top picks in their respective mediums, but here are some examples of music I love, most of which I doubt would be posted by anyone else here.
Anime:
1:25 is so emotional for me.
Games:
^ The male chorus that enters at ~4:52 here is reminiscent of the Soviet national anthem, which I love. This music is simply awesome.
Can't even mention great game music without appealing to FFVII for at least one example.