There is a stereotype that girls aren't as good at games as guys. I think this was born of the fact that girls just usually take games less seriously than guys.
I think this is more of a history thing. Most competitive players have 15+ years of gaming experience if not more. There are some exceptions, but generally the more experience you have the better you get. The problem is that gaming was almost exclusively seen as a hobby for young men during the SNES and N64 eras and not a lot of girls played games (it was actually much less true in the NES era and before, loads of girls played games then, unfortunately most of them seemed to quit during the 16-bit console war). This results in very few female gamers who have played games for that long.
These days, systems like Wii and DS have shown that the gaming audience can be a lot more diverse than this, and as a result you're seeing way more girls playing games. 15 years from now, girl gamers probably won't be anywhere near as uncommon as they are now.
Another stereotype is that guys are physically stronger/ more dexterous than females. This one is without a doubt very controversial, but heavily based in fact as well. Guys naturally lose weight faster, build muscle faster, and develop muscle memory more easily as a whole.
The notion that physical prowess somehow affects gaming skill is hilariously jokey. Have you seen us? Gamers on the whole aren't exactly the pinnacle of physical fitness and athleticism, and those handful who are in good shape don't gain any advantage from it. You need fast fingers and reaction time to be a gamer and that's about it.
Now, the one thing that might be a factor is testosterone. It's well known that testosterone influences competitive behaviour and men have more of it (on average) than women. But there are still plenty of women athletes or women executives / politicians who in no way lack for competitiveness. I still think it's mostly that history issue + ongoing sexism in the community.
