Is it bad to leave your computer on during a thunderstorm?
Most power strips don't provide surge protection, and then those that do provide a very basic level of protection. UPS battery backup units usually provide far better protection, but they themselves can also be damaged.
The best approach is to shut off your computers during a storm, and disconnect all the power cords (computer, monitor, speakers, printers, and other connected peripherals, etc.).
The risk is serious, and taking a short break from the computer to enjoy nature's power can actually be a really nice change of pace once in a while.
(As per comments below, I've added a picture of a good power bar to my answer here...)
You're probably not going to find a surge protector that can stop a direct lightning strike. A lightning strike is anywhere from 1,000 to 100,000 Amperes with rise times measured in microseconds. Too high and fast for most/all surge protectors, and that's why many people suggest unplugging.
Since lightning strikes are rare (especially direct strikes) a standard UPS with decent surge protection is going to protect you against lesser (more common) surges, and is definitely worth having.
In the end I think it's choice and risk mitigation. If you have home insurance that would probably affect your choice (insurance will replace the hardware anyway), and you can mitigate your data loss risks by having backups, etc.
Check out this article, it's got lots of good 'lightning vs. computer' information.
Certainly @Randolf Richardson provided a good answer, but i'd like to add that disconnecting all connections that come in from outside is good practice. This means coax, DSL, etc. in addition to your AC lines. That's not to say i always do this, but that's why i've had modems and Ethernet cards fried.
- Shut it down.
- Pull the main power strip plugs from the wall
- Disconnect coax from the cable company or DSL from the phone company.
- Now go do the same for your TVs etc.
Even with your surge-protecting powerstrip or a UPS, you could still benefit from disconnecting during a storm; a direct or near-direct lightning strike could blow through your consumer UPS pretty easily.
(On a related note, if you know a bad storm is coming, make sure laptops, phones, camera, extra batteries, etc. are all charged.)