I have in the past had gravity-served beer – often Draught Bass – which had little or no head but was perfectly fine, with an almost vinous character. That’s not something you come across very often now, though. Last year there was some discussion in the blogosphere about the Bree Louise in London, a Good Beer Guide listed pub that some rated very highly, serving cask beer that came out looking completely flat. I can’t see many people in the North-West finding that acceptable.
This also seems to be an issue with quite a few bottled beers. For example, I recently had a bottle of White Horse Wayland Smithy where the head had completely disappeared within a couple of minutes of pouring. It also afflicts quite a number of beers from the Marston’s stable – see my review of Pedigree VSOP, although more recent samples have been better. Another one is Budweiser Budvar, regarded as one of the best widely-available lagers, described by Tandleman in the comments here as having “a head that lasted a millisecond”.
Clearly there’s far more to beer than just having a good head, and there are plenty of indifferent beers where the head is about the only positive thing about them. However, regardless of a beer’s inherent qualities, the absence or rapid loss of a head invariably gives a poor impression, and in the vast majority of cases is a sign that there is something amiss.