Is it acceptable to start a sentence with “however”?

The Grammar Girl has a good article on this topic, basically:

It is fine to use however at the beginning of a sentence; you just need to know when to use a comma.

If it means "to whatever extent", don't use a comma:

However wrong it is, I will say it loud and clearly.

If it means "nevertheless", use a comma:

However, I don't give a damn.

I think this advice comes from the (somewhat strange) idea that sentences should have one complete idea. If your sentence begins with the conjunction "however", then it's an extension of the idea in the previous sentence and is therefore not a "complete idea". The same reasoning is behind advice not to begin sentences with "or" and "and".

Of course this advice is silly because sentences and "complete ideas" don't always line up, and there's no reason that a conjunction can't join a sentence with the previous one.