What types of punishments are there in the Babylonian king Hammurabi's code? Death, for example, was one type of punishment. What are others?
Hammurabi's Code is fairly concise, there are 282 laws, all of which are very short (certainly by today's standards).
You can read the whole thing in a few minutes here.
To answer your question: Mostly death and financial or property compensation. Although 282 has an interesting punishment:
If a slave say to his master: "You are not my master," if they convict him his master shall cut off his ear.