Separation anxiety is totally normal at this age, but the level you're describing sounds a little extreme. My first guess, just based on what you said, is that somehow his trust has been undermined. When you leave him with someone else do you sneak out or do you say goodbye to him? Parents tend to think it's easier if they sneak out, but if you do this you undermine your child's trust and they begin to fear that you will sneak away any time they can't see you (like when you put him to bed and leave the room). He will cry when you leave him either way (either when he sees you leave or when he realizes you're gone), so make sure you say goodbye and let him know you'll be back soon, but make it short and sweet.
In the mean time, if he is really truely upset at bed time, go back in and reassure him. You know what I mean by truely upset- as parents we learn to decode our children's cries, and I know when my daughter is really upset or she's just crying because she wants to put off going to sleep. If, for a week or so, you go into his room and comfort him every time he cries for you, you may reestablish his trust and make bedtime easier for both of you. But when you go in don't let him get out of bed and avoid picking him up if possible. Comfort him with as few words as possible (pat his head or back) and the second he is calm let him know it's time for sleeping and you'll see him in the morning, then leave. But go right back if he starts to cry. You will be able to tell when he transitions from being really upset to just crying to get you to interact with him/put off sleeping, and at this point you have to let him cry, but you will have reestablished his trust so the crying won't be as bad.