Action games are all about reflexes, the idea is to be quicker than the next guy. Needless to say, action games are more sensitive to your net connection than any other genre, so if you're not getting a smooth game you should look into upgrading. Historically, strategy games have been about using your brains to outwit the other guy, thinking ahead and working toward long-term goals in order to win the game. RTS games are still about planning and tactics, but there's a lot of quick thinking and fast mouse-clicking required to topple your opponents. Strategy games are a blast over the Internet and aren't usually as sensitive to your network connection speed as action games.
Tactical games are a unique mix of action and strategy.
Usually tactical games are based on stealth and teamwork, where you're working within a small team, or leading a small team, to accomplish a difficult mission while outnumbered. Needless to say, these games are perfect for multiplayer. For the most part you can't play them on the Internet, but a lot of the old classic arcades can be simulated on your computer. Skip down the page a little to our RPG section, which is probably right up your alley. Flight simulators are among the most popular, though a detailled simulation of driving a car, a tank, or futuristic vehicles like mechs all fall under this category.