Snape has always been a bad guy. He has treated Harry horribly from the beginning. It stems from a hatred of Harry's father James and godfather Sirius Black. They were all classmates at Hogwarts. Snape was mercilessly picked on by James and Sirius, among others, while they were in school. Now Harry is feeling the brunt of Snape's vengeance.
Snape begins to reveal the depth of his evilness in The Order of the Phoenix.
Sure Snape has done some mean things to Harry in the first four movies and books. Snape has taken away points from Harry's house, accused him of stealing potions and given him cruel detentions. But none of that compares to what he does to Harry in The Order of the Phoenix.
But it's what Snape does in the Half-Blood Prince that makes him a truly evil character.
He kills Professor Dumbledore.
For those of you who only watch the movies, sorry. Big spoiler there. But for the rest of us who are two books ahead of the movies, this is Snape's most evil deed.
There is no way to justify murder. Snape commits the greatest betrayal, the most vile thing one person can do to another: take his life.
For this reason and this reason alone, Snape is an evil character. He is a death eater, will always be a death eater and Dumbledore was a fool to trust him as long as he did.
It's not the only foolish thing Dumbledore has done throughout the books, but that's another discussion.
Suffice it to say Snape revealed his true self in the Half-Blood Prince: a cowardly, vengeful wizard looking to save his own skin rather than sacrificing it for the good of others.
He is the one character who deserves to die in the Deathly Hallows. Although I have a feeling his fate lies along another path.