Invincipigs
Invincipigs, also known as invisipigs, invincible pigs or client-side swine, are God's punishment for our sins on Earth. Before the Beta 1.7 update, these little nuisances appeared any time a mob spawner was placed on grass with a light level of 8 - basically, the same conditions in which normal, cute, delicious pigs are spawned naturally. Invincipigs, however, were a bug in SMP, one that Notch will answer for on Judgement Day.
Invincipigs and You
Invincipigs are (hopefully) a thing of the past. This is what they were like back in the day:
Invincipigs spawned because Minecraft told them to - but not the server! Unlike all normal mobs and actions, which sync with the server, invincipigs were client-side, meaning only you could see them (anyone else in the room saw completely different invincipigs!). They were completely impervious to damage - swords, arrows, fire, lava, you name it - and countless copies would bounce around and oink in an awful cacophony until you fled the area screaming or logged out and back in. This made using spawners to farm sheep an annoyingly amusing spectacle, necessitating fighting your way through herds of pigs to reach a single sheep.
What to Do In Case of Invincipigs
There is nothing you can do. Accept your fate.
(Or try not placing spawners on grass).