[elihu]

One useful heuristic (at least, the one I usually go to first if I'm not sure what key a song is in) is that root of the final chord of the song is often the same as the root of the key. I suppose that probably works better for some music traditions than others. Also I believe some songs in a minor key sometimes end by converting the root chord to major.

[dizzystar]

This is a good point, though there are many common patterns, some start at 1 and others do not.