Like the title says, what Albums (i feel songs would simply be too specific) could you not live with out?
Personally I'd have to go with:
A Fever You Can't Sweat Out - Panic at the Disco.
Whatever People Say I Am, That's what I'm not - Arctic Monkeys
Tonight - Franz Ferdinand
Liebe Ist Fur Alle Da - Rammstein
System of a Down - System of a Down
and...
Yeah, that's about it.