"Aitch", because that's what I was taught was right, though it's not logical (I mean I'm sure there's a historical explanation, possibly involving French, but on the synchronic face of it it's not logical). I think I might happen to say "haitch" in a moment of distraction.
(Presumably you're more interested in what native speakers say, but I thought I'd reply anyway. I did cast a vote, too. Edit: Ah, votes are public, so you can see it already.)