You should be cautious when purchasing any console, but I've had mine since February with no problems. You rarely hear of no problems, but people with problems won't stop talking!
How many people own these? How many complaints have you heard? Bad batch(es) anyone?
Also, remember when you buy the console and the salesman starts blabbing on about extended warranties? Listen to them before you say no, because it will save headaches if you do have problems. Sure it's a gamble whether it will ultimately be worth it, since the likelyhood of a problem is small, but it's not a monthly insurance fee and if you buy from a reputable location you'll be able to walk out with a brand new console the same day you have problems, rather than waiting a month and paying $150 to get a refurbished (not new, had problems already, might be fixed) unit from the manufacturer.
As long as it starts at the end of the manufacturer's warranty period it might be worth it just to be sure. The 360 is still far from being a cheap, easily affordable console and if something goes kersplat on day 370, well lets just say the language probably won't be "work safe" ;-).