You use compression for way more than just drums.
First off, there are two kinds of compression: when you're tracking, and when you're mixing. Some people don't use any compression when they're recording, but they've got better control over their levels than me LOL. I put some mild compression on vocals, for example, in order to avoid clipping. I test the level before I record so that peaks are hitting somewhere between -6dB and 0 dB, but I always seem to put a bit more energy into it when the machine's actually recording, so a bit of compression (3:1) helps keep the levels inside the line.
As for mixing, there are different uses for compression. One of the most common is for getting more control over the level of a particular track - to tame the kinda wild dynamic swings. For example, you want the vocal to get heard in the mix, but sometimes when you're singing there'll be really loud bits that you see as spikes and peaks in the waveform, and then there'll be the quiet bits that don't get heard. So you compress the vocal track in the mix. What does that do? Well, it squashes the track so that there's less distance between the loud peaks and the quiet parts - the result is that the loud parts don't sound so loud in relation to the quiet parts. Plus there's this extra benefit: you can turn the whole track's volume up, and it still doesn't clip. And the wonderfulness of this is that it makes the vocal louder in relation to the rest of the mix - the quiet parts are louder and get heard. This gives you way more control over what level you choose for the vocal track.
Drums and bass are two other places where compression is common.
As with all effects, compression is best used most of the time in small amounts - the less, the better. Use it when you need it; don't use it just cuz it's there.