There are a couple of things that you should know to keep your 360 running:
1. A good warranty from the retailer you bought it from.
2. Never have your 360 on the carpet.
3. Never have anything surrounding your 360. Let it have breathing room.
4. Like 2Good4U said never tilt your 360 when operating. If you do then you will hear a loud grinding sound which is not good.
5. Take a break between long gaming periods to let the 360 cool down. Maybe 5-10 minutes is enough. You dont have to do this but it would help increase your 360s life span.
If you havent got a extended warranty yet I would. If you can get it from the retailer you bought your 360 from that is the best option. If its too late for that dont feel down my friend there is another option. Just call Microsoft and buy the 1 or 2 year extended warranty. I had to send my 1st 5 360s in for repair because of different reasons.(over-heating, freezing, no picture, etc.) I bought the 2 year extended warranty from Microsoft for about $60.00.
If you are worried about your 360, I strongly recommend that you get some kind of extended warranty.