In Voyager, we primarily see various gourds and other alien vegetables in Neelix's kitchen, and most of the food we see replicated is vegetarian, like an instance of Paris ordering tomato soup, though Paris also does at one point express a craving for pepperoni pizza, and Neelix in another episode regrets to inform the Markonian visitors that has has run out of "marsupial surprise".
In ST VI, the dinner scene shows mostly unrecognizable blue food, probably a pasta of some sort, and nothing identifiable as meat. Similarly, in the galley scene later in the same movie, most of the food seen is either vegetable or baked goods. ST IV has the pizza and beer scene, and of course they have to take the pizza to go, so we don't know if Kirk likes pepperoni (Memory Alpha asserts that Kirk, despite claiming to like Italian, was unfamiliar with the size of a full pizza).
I can't remember much eating in TNG (Captain Picard seems to subsist solely on Earl Grey tea IIRC); what I do remember humans eating was mostly unrecognizable, but definitely not meat.
The main source of meat-eating in the canon is in DS9 (which in general has a lot of societal differences, like the existence of real money, from other ST series): Sisko's father is a Louisianan, and has a Creole restaurant in New Orleans, which from our sensibilities would almost certainly include fish and shellfish, but maybe not. In the episode of Worf's "bachelor party" and wedding we see plenty of meat, which O'Brien and Bashir certainly don't turn their noses up at, but it is a Klingon ritual after all (however Bashir proceeds to order a steak from Quark when it looks like the wedding's off).
So, while there are a few references to meat sprinkled through the canon, primarily recently-written canon (DSY/VOY/ENT) and often in reference to one or more alien races, it seems that animal protein is a rarity for humans through most of the canon. I can think of two reasons:
Most of the canon takes place aboard ship; even for senior officers, meat aboard a starship 1000 light-years from the nearest industrialized planet, would be a rare delicacy.
The human race, in its societal turnaround from near-self-destruction after meeting the Vulcans, largely lost their taste for red meat, focusing on different, possibly less environmentally harmful, forms of agriculture.
Earlier canon seems to indicate more the latter, while episodes and movies written after Roddenberry's death seem to take more license and the lack of meat is due to practical diufficulties. Anyone have any official sources on this topic?