Agree with @michaelk -- my Dell lap top is running 24/7 with no problems.
Here are some things to think about, though.
You want to make sure the thing isn't cooking itself so keep the ventilation slots clean and not blocked by dust or "soft" material; set it on a hard surface, maybe put something under the feet to raise it off the surface so air can get into it. If it's hot to the touch, that ain't good and you need to do something about that. If the fan runs frequently that's a hint.
What's it doing? Do you have some application running all the time? Not the normal processes that are sleeping most of the time and wake up every so often but something compute-intensive? You might want to add a monitoring utility and keep an eye on things -- one oldie but goodie is
GKrellM (
http://members.dslextreme.com/users/...m/gkrellm.html); it may already be installed on your machine or you can download it from the link. It's a display that shows system activity, your CPU cores, processes, disk activity, network activity, temperatures, memory, battery, all sorts of stuff that shows at a glance what's going on. Your CPU cores should be idling along at about 1% or less most of the time -- if they're cranking at 50% or higher, you've got a problem to deal with (heat's a killer).
Have you configured power management? There should be a utility for doing so, check your distribution documentation.
Disk drives do break, it happens. The drives in lap tops are physically tiny little things and any number of things can make them go bad (starting with the manufacturer). Lap tops can get dropped while turned on (or off, too) and disk drives don't like bouncing too much. Back up stuff you care about.
Batteries go bad too. It happens. It used to be a good idea to charge them, let them get down to almost empty, charge, and repeat that for a week or two. Anymore, that doesn't apply and you can leave the external power attached and keep them charged.
Again, it shouldn't hurt to let it run, just make sure it can "breathe."
Hope this helps some.