What are the Altars to Kali for?

Damaging an altar (either with bombs or by enemies/traps while you're in the level) will result in punishments:

• Damage an altar once and you will get a lot of spiders after you.
• Damage once twice and you'll also get a ball a chain that you have to drag around the level.
• Damage one a third time and the level will also go dark and a ghost will be summoned. Unless you're right next to an exit you are unlikely survive this.

Sacrifice items to an altar to get rewards:

• Drop a gold idol to get a golden monkey that runs around the level crapping gold. I think this might eventually net more gold than the idol would have given you, but it's hard keeping the monkey alive.
• Drop a stunned (or dead) enemy to please Kali a little.
• Drop a stunned damsel to please Kali a lot - one damsel is enough for a random item reward.

Please Kali enough and you get the Kapala - a skull cup that gives you back health from bleeding enemies.

In the original Spelunky they were all the things were worth sacrifice points, I believe the Stunned Damsel/Idol were 8 (if dead the damsel is worth 1 or 2, the same goes for regular enemies, alive they are 2, dead they are 1) I have a feeling a stunned Shopkeeper is also worth 8, at 8 sacrifice points Kali gives you a random item, at 16 (2 damsels) you get the Kapala, I think at 32 (4 damsels) you get an extra 8 lives, I believe the Throne in the Black Knights castle acts as a regular altar.

http://spelunky.wikia.com/wiki/Altar

In addition to the other answers - if you are playing split-screen, try putting your friend on the altar. Guaranteed item at the cost of a friend!