Skills like hand-eye co-ordination, improving your reaction speed, and stuff like that? Hells yeah. I have really good skills like that, which I put down at least partially to my habit of playing video games.
However, skills like firing a weapon or learning to drive or do parkour? No, games can't teach those skills. However, they can teach the basic ideas and concepts, provided the game is realistic enough and/or is a simulation of some sort. For example, I learned to fly a glider when I was 16, and I've since found the experience of actually flying to be very similar to games I've played like H.A.W.X. and Star Wars Starfighter. But of course, playing those games can't teach me how to actually fly a glider, the concepts are similar but the actual execution is very different. As another example, I learned how to fire weapons such as the L-98 rifle, and again the process of aiming and firing was similar to what we see in games like Halo, but there's no way those games can teach me how to really aim a (heavy) rifle and accurately fire on a target. And of course, games don't teach you how to strip down and clean a weapon or do maintenance checks, and game developers have apparently never heard of safety catches either.
For the record, I don't count games like 'Cooking Mama' or similar stuff in this post. Such games can teach you skills, but that's their entire point anyway so shouldn't really count here, right?