Let's see:
These inflict damage: Burn, Poison, Confusion, Badly Poisoned, Curse, Leech Seed
These cause damage: Magma Storm, Whirlpool, Fire Spin, Wrap, Bind, Clamp, Sand Tomb
So: Badly Poison, Confusion, Leech Seed, Curse, and Magma Storm/Whirlpool/Fire Spin/Wrap/Bind/Clamp/Sand Tomb can stack.
Edit:
Binding moves do not stack.