It depends greatly on the game and the device/platform it is on. But I've heard almost all kinds of music in video games. I agree with the other posts - we need a bit more info to know what you're really after. Are you asking as someone who's studying to become a game composer? Are you asking as someone who's writing a research paper on the topic? Are you just curious? Tell us more and we'll be able to help you more.

The smaller the budget, the more likely that the music will be electronic, since that is essentially the lowest common denominator in music creation (not that it's all bad...there is certainly really great electronic music in some games).

Do you mean virtual? Because I've seen some really low budget games with various genres of music supporting them. I don't agree that low budget games means the OST will likely be electronic at all.

Music recorded live, especially with mostly acoustic instruments, is not real common in games. So, not lots of rock bands, jazz trios etc.

Where are you getting this information? Because it's simply not true. I can list off a ton of games, mobile/social and triple A level titles, that use live recordings. I have personal friends who have used full orchestras for their game soundtracks and some of these were even for iPhone. And I've played plenty of games that had metal/rock soundtracks. Even a few games that had jazz ensembles, although I'd agree jazz is a bit less common than rock/metal/orchestral. Even hybrids are especially common - where they use orchestral combined with distorted guitars/etc.