It's both much simple
r and more confusing than any of you imagined.
Herb is standard American English; a 1993 pronunciation survey, ~90% of Americans said herb without the 'h'. (The proper name, Herb, keeps it pronouced.)
Herb is a fine example of a type of linguistic conservatism found in American English. Until the sixteenth century the word was usually spelled "erb"-- it was a French word, who didn't say the "h" either. Right up until to the nineteenth century, long after the 'h' had been added due to further icky French influence, that was also the way it was said. "erb."
Seventeenth- and eighteenth-century colonists toward the Americas took their pronounciation with them. During the nineteenth century, the British people started to sound the first letter, in a "spelling pronunciation."
So, the Americans are saying it the old fashioned way, and the Brits are playing around with their new-fangled words.
So, Eddie Izzard wasn't off saying that "We say herb like that because there's a fuckin' 'H' in it."
Now you know.
Some additional information, because it came up on slashdot, I looked up some stuff on the a v. an debate:
From my Usage Dictionary (M-W Dictionary of English Usage):
1. Basic a/an rule, a before initial consonant, an before the vowel
2. Before h in an unstressed or weakly stressed syllable, both are used writing, but an is more common in speech, whether the h is pronounced or not. Due to some historical reasons, h is not really pronounced. A few words, like historic and hotel (esp. in England) are in transition, and both can be found. Choose the article that suits your pronunciation.
3. Mentions usages in words with silent h's and stressed sylables (esp. in the bible). Use article per your pronunciation.
So, basically, either is "right" with herb. Choose the one you feel most comfortable with. And, if you're really curious, my usage dictionary has almost a half page on the issue. Pick one up, and be pretentious occasionally.