1. Dr. Gregory Yates
Gregory Yates (Dallas Roberts) is the worst. The character was a rapist, stalker and serial killer, and he taunted members of the IU repeatedly during seasons 2 and 3. He stalked Lindsay for over a year, but the truly unforgivable crime he committed was killing Nadia Decotis (Stella Maeve) in season 2.
Decotis was an administrative assistant for PD during the early years of the show, and her death came as a shock to fans and officers alike. Thankfully, Law & Order: SVU came in and helped to formally charge Yates with murder before locking him up. Or at least, trying to.
Yates escapes, and eventually gets put down, for good, by Lindsay. It's an emotional moment for the character, who was close with Decotis, and it's comforting to know that the criminal can't inflict any more damage.