I believe I read that after X hours of playing Team Fortress 2 in a period of Y days, you stop finding items. How long do I have before I stop finding items? And if I hit this limit of gameplay, how do I tell?
According to the official Team Fortress 2 Wiki page:
The current item drop system was introduced on April 20, 2010. Players are guaranteed to find items at regular intervals of 30 to 70 minutes, with an average interval of 50 minutes. [...] There is no cap on the amount of items that can be received per week, but instead a cap on the amount of playtime in which drops can occur. This cap has been estimated to 10 hours each week ([resetting] every Thursday). Playing beyond the cap won't yield additional items. Playing less than the cap carries over unused time to the next week, increasing that week's cap to a maximum of two weeks' worth of playtime. [...] Receiving a Mann Co. Supply Crate or any usable item does not count against the cap...
And to answer your question of "and if I hit this limit of gameplay, how do I tell?", I guess you could time yourself playing for 70 minutes, and if you don't receive any items, you've hit the cap.
To make it simple, yes there is a limit of normal items (weapons and such) but it capped with time. as stated above, 10 hours weekly, with the timer resetting at 00:00 Greenwich time (7pm EST), Crates and items like that though are own its own system, and will still drop after the 10 hour mark.