(Like all my other stuff, this isn't meant to be taken super-seriously, just my personal views.)
I've always hated that parents and teachers blame teen violence on video games, it's like the industry has a big red bulls-eye on its back and no one can take it off no matter what. I've repeatedly tried to explain that games aren't pure evil, don't turn every child into a killing machine, and are actually good for you if you know where to look. Well, I've failed to convince my folks but, in hope that someone out there will succeed, I've put together a tiny 'list' of arguments. (If anyone actually manages to change someone's mind, then you're a hero!)
Unlike watching a tv show or a movie, when you play a video game you actively involve yourself in the virtual world. When you watch a movie you basically just sit there and enjoy the story told, but a video game forces you to interact, think differently and find solutions by yourself.
Different games develop different skills, it all depends on what you pick. Platformers help you think creatively since you have to observe, figure out where you need to go next with only the few abilities that your character has available. They also test your dexterity, speed and so on. Ever successfully finished a series of acrobatic jumps only to fail the last one because you weren't fast enough? Real life doesn't give you a second chance, but thankfully video games do. This way you can learn from your mistakes and perfect yourself.
--Put on your strategy hat--
RTS (real-time strategy) games can be a little tough if you hate strategizing. I prefer to play along with another person so that putting together a tactic feels more real. For a while, these kind of games made me automatically search for weak points in real buildings and, though annoying, made me feel like I was developing some special skills that others were unaware of.
I personally hate being a leader, but RTSs brings out this trait in anyone; you feel responsible for every defeat, no matter how small, you constantly try to think of a strategy that can outsmart the enemy. And the sense that you get when winning is pretty overwhelming, especially if you've played for a long time. Any loss just makes you want to push on and get passed that stage, it's a constant battle of improving yourself and moving on. So this is why I say that video games help us become more motivated, they basically stimulate this
For a while I didn't know why musical video games were so popular. While Guitar Hero doesn't really help you learn how to actually play a guitar it does amazingly improve your reaction and speed. I have horribly slow reactions, but take my word for it: Guitar Hero can turn anyone from a lazy couch potato into a hyper little puppy. It's one of those games that are incredibly easy to learn but hard to master. I was amazed at how quickly my fingers moved on the fret as if by themselves, and I was having fun at the same time. Now that's fun learning at its best.
Tetris and all the other classical games are obviously there for improving your thinking speed, but I prefer to talk about newer games that combine graphics with skill-learning.
I personally love a game that lets you drastically shift the story in the direction you want it, and none do it better than the adventure/mystery/detective genres. Point-and-click, third person, it doesn't matter, they all have their own charm and they all put your brains to the test. The Broken Sword series lets you work with dozens of items that you can combine and use all over the game universe. But it's your job to cleverly combine them and figure out when and where to use them. And when you throw some humor into the game the experience just gets more enjoyable. Any idea what you can do with theater paint and a cheap statue? How about a tiny tequila worm? Well, you'll have to play the games to find out.
The Longest Journey also puts your wit to the test, and always makes sure that you're on your toes. You're often stuck in an unfamiliar territory with a limited amount of items and you're left to try and figure a way out yourself. I can't say that it prepares you for similar situations in real life, but it certainly gets the cogs moving and your creativity going.