if it is doing something that makes the hardrive spin then the hardrive will reach the end of it life sooner, if the screen is on all the time it wouldn't be that good either, you can put it to sleep when you don't use it. That said, i keep a laptop on for 3 years 24/7 until the HD died.
I had a dell Inspiron 4100 which ran 24/7 for about 4 years. The HD just died this summer and deep inside i'm glad. I was begining to think Dells were invincible. Good bang for the buck.