Best Tools for Finding Your Bearings
Every phone has a magnetometer, so the compass app argument is over. What is worth saying instead is that a compass app and a compass are not the same tool, and knowing which you need is the useful part.
What the phone is good for. Telling you which way you are pointing when you step out of a metro station, or orienting a map on screen. The built-in compass on both iOS and Android is fine for this and needs nothing installed.
Where it lets you down. A phone compass drifts near anything magnetic, wants recalibrating constantly, reads badly when the phone is cold, and stops entirely when the battery does. It also cannot take a bearing and hold it while you walk, which is the actual skill navigation depends on.
So for anything off a marked trail, carry a real baseplate compass. A Suunto or Silva with a rotating bezel and a sighting line costs about $20, weighs 30 grams, works at any temperature, and has no battery. Paired with a paper map it does something no app does: lets you take a bearing off the map, follow it across ground you cannot see across, and know roughly where you are by resection when you are lost.
Two things worth setting once. Learn the difference between true and magnetic north and check the declination where you are going, because in parts of the world it is large enough to walk you into the wrong valley. And practise on a walk you already know, not on the day you need it.
The gadget answer to this post has changed completely. The advice underneath it has not moved at all: the compass that matters is the one you can use without thinking.
Part of the guide to trekking and outdoor kit.