Paul the Wine Guy was the first of many men whom Monica dated on the show. He appeared in The Pilot as a date of Monica's.

He worked in a restaurant with Monica and she had probably told her friends about him prior to the episode since they all referred to him as "Paul the Wine Guy". They went out for dinner, but Monica insisted it wasn't a date, just "two people going to dinner, and not having sex," to which Chandler responded by saying "Sounds like a date to me." On the date, Paul claimed that "Since my wife left me, I haven't been able to perform... sexually". They ended up having sex. However, a co-worker of Monica's who had also once had sex with Paul had prior to this been told exactly the same thing-it was a line he used in a clever scheme to get women to sleep with him. When Monica discovered this after a casual conversation with the co-worker in question, she angrily breaks Paul's watch with her foot. Never to speak to him again.  

It is never explained why he is called "the Wine Guy". Phoebe even asks Chandler "What does that mean? Does he sell it, drink it, or he just complains a lot?" but she doesn't receive an answer, as Chandler doesn't know.