In terms of dangerous situations or harm to people, they are pretty similar. But Jeopardize is used in a wider context. Danger tends to be used for living things, where as Jeopardy can be used for Economy, finances, relationships etc A stunt like that could jeopardize the financial future of this company!

I'm with Paul. "Jeopardize" can be either inanimate or living things. "Endanger" is usually said when it is referred to a living thing and is usually meaning that they could die, not just be in trouble. "Endangered species" is a common expression for animals that are about to be extinct.