Some games are better than others. Battlefield 3 has really good character animations for the most part, although you notice it less because it's not an NPC-dialogue heavy game. Deus Ex on the other hand, has some of the worst NPC-dialogue animations of any game I've ever played: bad lip sync, fidgety characters who look like they are constantly uncomfortable.

I haven't played Skyrim so I can't really comment on that. Oblivion had fairly decent character animation but it was mired by moon-physics: NPCs eagerly charging down stairs (or off a small ledge) to engage a foe would sort-of float and there would be this "running in the air" effect that was especially noticeable at the very beginning of the game.