Well, here's a list, but ultimately they all died of heart failure, just like you and me:

shot
old age
drowned
buried alive (got an felony animal cruelty charge on this one!)
burned alive (ditto)
slaughtered, cooked, and eaten
run to death
dog fight
lethal infection
run over
left in the country because "the farmers will take care of it"
gassed
eaten or mauled by wild animals
hung (see felony, above)
cancer, distemper, and other diseases