It's shown that spike can survive for a long time without supply of fresh blood. It's never really stated what happens if vampires don't feed.
What does happen?
Do they need to feed?
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In Buffy 4x08 ("Pangs"), it is mentioned that a vampire who is starved is like a "living skeleton" - they won't starve to death, but there are definitely adverse effects to starving.
Later in Angel 3x22 ("Tomorrow"), Angel is sealed in a metal coffin and thrown into the ocean. In 4x01, you are presented with Angel's hallucinations while he is trapped and starving - these hallucinations continue after he has been freed and fed animal blood. Wesley eventually figures out that it's not strong enough, and feeds Angel some of his own blood.
Vampires which don't feed in Buffy can't actually die (as 'hunger' isn't on the list of things which kill vampires), but they'll suffer hunger normally - i.e. become emaciated and powerless.
The only dialogue I remember referencing this is in series 4, during the Thanksgiving dinner in "Pangs":
SPIKE: You know what happens to vampires who don't get to feed?
BUFFY: I always wondered that. Giles, plates.
SPIKE: Living skeletons, mate. Like famine pictures from those dusty countries, only not half as funny.