We use them for our snakes, and yes, we leave them on 24/7. we have not had any problems related to them in the 7 months we've been using them on our snakes.
mind you, we read over all the instructions carefully, and the only thing they said was something like "continous operation will shorten service life". nowhere did it say "do not use 24/7".
at the rate our collection is growing, we will be going to heat tape prolly within a month or two anyhow.
It is a personal choice to use them or not to use them, and, as linds stated, its all in your comfort level and how much you want to risk.
as a side note, i've got little faith in the older heating fixtures. last year, when my timer went on in the morning, something shorted and the dome and wiring caught fire on one of my tanks. Thankfully i was right there and was able to blow it out before it got bad. Now, i make sure to only use new, ceramic dome fixtures in excellent condition. (common sense eh?).