A power failure can harm your computer, but it seems to be something of a random thing. Where I live, we get frequent power "blips", where the power fails for like a second, and comes back on - probably something touching the line. In any event, I ended up replacing my computer's power supply 3 times in 5 years before I got wise and got an UPS system. It also told me that the quality of the power was okay aside from the spikes. And yes, the computer was on a Belkin surge protector...
You might have gotten lucky this time, but don't assume that you're peachy. Get a UPS, even if it's a small one.