Esuohlim, that happens to me sometimes too. My advice to you, would be to simply fight your way through this tedious part, because it might get better later again. Sometimes all it takes is a half hour, and suddenly you're motivated again. Unless of course, you're simply tired of the game mechanics in every way 'cause there's no variety, and then you might as well give up.
Now to your question: It varies. Sometimes only one, sometimes as many as 4. I usually have one main game though, playing others a bit on the side. Some games I play sporadically. You know, nothing goes over a good round of worms for example. Mhhmmm...I gotta play some Worms again...now where did I put that CD...
I also just realized that I hadn't quite finished Mafia yet, and seeing how I've only got 2 levels left, I might as well finish it, even though I thinks it's way overhyped by most people.