| You can schedule things like disk defragmentation and virus scanning to happen late at night. You can leave your computer doing things like SETI@Home.
You don't need to worry much about fans wearing out. It just doesn't happen very often.
Unless you have a good surge protector, you should be turning off and unplugging your computer during lightning storms. If you do have a good surge protector (one that provides $$ guarantees if your system is damaged by lightning), then you probably don't have anything to worry about there.
Hackers you don't need to worry too much about if you're on a dial-up connection. If you're on cable or DSL, you should be running some kind of personal firewall anyway (there are a few, such as ZoneAlarm, out there for free).
My system is going on 3 years old and has been running more-or-less 24/7 for a great deal of that time, with no ill effects. | 
