Good question, they are similar. "Although" and "though" are practically interchangeable, I think. "Even though" is more emphatic. "Despite" is used a little differently (despite + noun or despite + gerund, I think) but the purpose is about the same. Seeing / hearing lots of examples is probably the best way to distinguish them. I think you can live without "despite" and "in spite of", but you can't live without "though".
( Although / Though ) I wanted to go to the cinema, I didn't have time.
Even though she had brought gifts, he did not invite her to the party.
Despite his illness, he went running in the afternoon.
Even though he was ill, he went running in the afternoon.
They walked home, in spite of the heavy rain.
They walked home even though it was raining heavily.
Note that "spite" by itself means dislike, hatred.