This article is from the Vegetarianism FAQ, by email@example.com (Michael Traub) with numerous contributions by others.
Finings are substances often added to beer (especially British beer
or "bitter") or wine during fermentation to help clarify out
particles and yeast, leaving the finished product clear. Finings
are not present in the finished product in any significant
quantity, their purpose is to settle out of the product, not stay
in suspension. OTOH, if a chemical analysis were to be performed,
there would probably be a few molecules of a fining agent still to
be found. Some finings are animal derived, the most common are
isinglass, made from the dried swim bladders of sturgeons, gelatin,
egg or blood albumin (in wines) and caseinates (from milk, also
used in wines). However many non-animal derived sources also exist,
the commonest ones being bentonite (clay), Irish Moss (a seaweed),
silicon dioxide and polyclar. Beer brewed according to the
Reinheitsgebot (German purity law) is not prohibited from using
finings since it was generally assumed that finings were not
present in the finished product.
Animal products are also sometimes used to alter the flavour of the
wine/beer or control the head on a beer. See the rec.food.drink.beer
FAQ for more details (where a lot of this has been stolen.-)
Most spirits/mixers are suitable for vegans, common exceptions
include some vodkas (may be cleared through bone charcoal) and
Campari (contains cochineal, an insect derived colouring).