I disagree with all that say a cheap compass is OK.
A compass is one of your most important pieces of survival gear, and if you have a good orientierring compass and a USGS map you can pretty much triangulate yourself in any situation.
I guess I should distinguish an 'inexpensive' compass from a 'cheap' compass the former (AKA any sylvia or millitary issue) will not freeze in cold temperatures, and will consistantly point in the same direction.
Sure all compasses do that, right? not really, I've had a compass freeze on me, and also a less expensive compass (really saved me about $5) be so weak magnetically that it got spooked by iron deposits, making it worthless.
If you have a GPS you should also have a compass, and you should always have a good map.
Well I don't mean to say you should buy a $100 lensatic compass with tritium vials or anything. But a good sylvia compass costs about $2-3 more than a cheap no-name POS.
Get something that is filled with oil (won't freeze) has some glow in the dark properties (you may have to use it at night), has a good base with ruler stuff on it (helps when reading a map to have some basis for comparison) and is made by a reputable company (you want a compass that points north, not towards your nickel belt buckle).
A compass is one of those 'save your ass' pieces of equiptment. You never need it till you need it badly, and I've been enough places with a lot of iron in the ground to know that there is a difference between a good compass and a cheap POS.
Just my $0.02
Best,
Todd (edgedance)