Like Hikin_Jim is with stoves, I am with compasses. I have one or two (or three or four ;-) from most of the major makers and lots of others. Lots of styles as well, needles, cards, baseplates, mirrors or not, lensatic, etc.

Brunton Pocket Transit - most used, but not ideal (too heavy) for the use I assume you are talking about. My most used compass other than that is an old Silva Huntsman. Small, easy to use (as either a baseplate or just a direction finder) and accurate, it works well for most uses. I always carry a more precise compass as a backup, they are too light to worry about not having extras. Most of the button compasses in my various equipment are removed (including the one in my RSK). I usually teach general navigation with the Brunton 9020G. Good and inexpensive (you will probably carry it a lot more than you use it) and has setable declination.

As others have said, it is truly terrain dependant how much you will need it, but when you do you want a good one. Precision is often important when you need to use a compass. On the great plains, on the arctic tundra, you can see a long way most of the time and your accuracy is less important. If you are in fog, a few degrees can make the difference between finding home or walking a lot then surviving :-) until the weather clears.

Good compasses are available from lots of makers, but in the US, don't buy a Silva marked compass. They are now made in China and broken ones are common. If you want a Silva, buy a Brunton or go overseas to buy it (I have bought several from vendors in the UK - gee the internet is great). Suunto is great (I love their wrist compass and the Arrow 6 is super for it's purpose).

Respectfully,

Jerry