Looking at Blizzard, they have a few positions that I could fit in immediately, but for everything else they require many years of experience. Going to apply there.
Valve have even bigger requirements, at least 5 years of experience for all available positions, so no point applying there.
DICE has some internships that I may fit in, but they require that candidates go to postgraduate education in Sweden (which is one of the countries I'm aiming at). I'll apply if I extend my education there.
Bethesda has a few interesting positions that don't require dozens of years of experience, so I guess applying there is an option too.
GG is out of the question, no open positions.
Tried twice at GOG, guess I'll leave it at that. :)

Are you guys familiar with some other places?

I assume you're looking for online positions, yeah? Because smaller studios such as DoubleFine might be more welcoming to newcomers, but they're also more likely to require you to actually come in to the office.

Don't have to be online as long as the said country allows foreigners to move in and work. So apart from some obscure countries, all are possible, I guess.

CD Projekt Red has a lot of positions open and some of them may be open to newbies:

http://cdpred.com/

I haven't really researched this sort of thing much, I only know about DoubleFine's due to obsessively checking their site. Their Jobs page is kind of awesome though: http://www.doublefine.com/jobs/

Lmao, that is pretty cool:)

Maybe RIOT is another good developer at which to look. Hi-Rez has quite a few irons in the fire as well.

I wouldn't pay too much attention to the years of experience requirement. The worst that can happen is you don't get a call back...

I think every job I've interviewed for had higher requirements listed than I had, but it didn't matter. I would try anyway, but remember that what distinguishes you from everyone else is passion. If you demonstrated a true love for what you want to do and use your own time advancing your knowledge, that will go a long way. Maybe even contribute to a few open source game projects.

The ability and desire to learn is more important than years of experience