This might be a stupid question, but I can't find the answer anywhere. Why don't objects such as rings that people wear (which are made out of metal) have electric current in them? As far as I know all the requirements are met (magnetic field exists, electrons can freely move).
A change of magnetic field induces a current, not the existence of the field itself.
That implies that if you move your metal ring around (like waving your hand) or change its orientation to the earth magnet field, a current will be induced; proportional to the change. When you stop moving, the current stops of course too.
What effect would you expect? If you do it a lot, the resistance of the ring will start to warm it up a bit. It needs a lot of moving to get any feelable effect though, as the earth's magnetic field is not very strong, so the current-inducing change and therefore the current are also not very high.
If you put an ampere-meter in the ring, you would be able to measure the current (but waving it around gets a lot more cumbersome, probably).
If you use a much stronger artificial magnetic field, make the ring larger, and move it around very quick, you will get a lot of current. That is called a Generator.