In addition to Jeremiah 1:5, already quoted by Jonathon, we have the case of the man blind from birth:
John 9: 1-3
1 And as Jesus passed by, he saw a man which was blind from his birth.
2 And his disciples asked him, saying, Master, who did sin, this man, or his parents, that he was born blind?
3 Jesus answered, Neither hath this man sinned, nor his parents: but that the works of God should be made manifest in him.
Since the man was born blind, and did not become blind later on, the implicit assumption here is that it's possible for a premortal sin to cause a congenital defect as punishment. Jesus didn't correct them by saying that there's no such thing as premortal existence, but instead said that the man's blindness wasn't punishment for any sin at all.
Taken together with Jeremiah 1: 5, we've got a fair amount of support for the spirit of man existing before mortality begins.