Angel was cursed as a vampire with his soul - which is why he was "special" and "good". He had to remember all of the evil things he did before he was "cursed" as torture.
There were several episodes where he lost his soul though.
It wasn't so much that he had to remember all his past evil deeds, but more that his soul also imbued him with a conscience, causing him to feel guilt and remorse (a lot of it, and all at once too).
