What does Germany do with draft-dodgers?

What happens to German men who are found fit for military service, but refuse to serve or perform any alternative service?

I assume you refer what’s called Totalverweigerung in Germany, i.e. not just being a consciencious objector and doing nine months of civilian social service instead of military service, but refusing all service out of principle.

The German Wikipedia article says the usual sentence for nowadays this is a suspended sentence of three to six months, or an equivalent fine.

Totalverweigerung is pretty rare, though, and done only by people who are opposed in principle to any compulsory service, or to any legal authority.

Using the official conscientious objector procedure is much more usual - in 2005 137,000 draft-age men did that (cite - German language), plus 1639 serving soldiers and 492 reservists. Conscientious objectors serve their terms mainly in social services, hospitals, as ambulance drivers etc; you can alternatively sign up for serving a certain number of hours in Katastrophenschutz (civil defence/emergency response), and in a number of other roles (including foreign aid - my brother fulfilled his obligation by working with homeless people in Washington D.C.)