I went through the TVTropes links, as well as Memory Alpha, Internet Movie Database, and the Wikipedia Star Trek: The Next Generation Episode List to check episode summaries. If there was any doubt, I pulled out my ST:TNG DVDs and skipped through the episodes for reminders of the storyline, just in case there might have been a Wesley B-Plot (or even C-Plot) that I may have forgotten.
I found nothing on TVTropes to support their claim of Wesley holding the record for romantic liaisons on Next Generation. I did find the following:
The Dauphin: Wesley becomes romantically involved with Salia, the titular character. There's no indication he had sex with her, but it was clearly romantic.
The Game: He bonds with Ensign Robin Lefler. There's no indication the relationship continues after Wesley leaves the Enterprise at the end of the episode. It's not clear if they ever slept together and it could be argued there was a friendship and not a romance.
The First Duty: I don't think there was a romance going on between Wesley and either of his female crewmates in Nova Squadron. It's possible, since there are times it seems like there might be more, but that is likely just the closeness team or crewmates in such a situation would develop normally.
Other than that, I could not find indications that Wesley was in other romantic relationships.