I'll take comic disagreement with DA01, and say that any reasonable person knows what reasonable means.
To answer the question about placing limits, the answer is yes . . . but like everything else, all things in moderation. Limiting after school game play to that magical time between when they get home and when you get home is reasonable. OTOH, Kicking the entire console out the door is not reasonable.
Any limitations should be placed with a dose of realism. The above example of "the time right after school" sounds ridiculous... "They should use that time for homework! And chores!" and that's right, they should. BUT, like most latchkey kids, they're unsupervised during that time. Attempting to impose a limit when nobody is there to enforce it is a setup for failure.
You can easily parent into it though:
You know what you should do? You should do your homework first thing when you get home, then you don't have it staring you in the face to do later after I get home. Now, you know you're supposed to turn it off after we get home and I've noticed you hemming and hawing about doing your homework at that point, probably because you're still jazzed from the game. But if you do it early and get it out of the way, I have absolutely no problem comping you the game later on.
You're being reasonable by allowing them to play while you're not there. It's not out of the question to expect them to be reasonable as well. At 10-12 (preteen yrs) I think it's a good idea to communicate that expectation.
Of course I've elaborated on a single scenario. I think the point is that you can set a limitation that makes sense and is achieveable. You might even discuss some options and come to some kind of systemic agreement with your kid.
As far as getting rid of it altogether, I think that would be a big mistake. For a preteen, it could easily sow interpersonal issues completely unrelated to video games and could develop into a serious, long term wedge issue.
Bottom line: be reasonable with your limitations and you should get a reasonable response.