Herd is listed as having won the Asian Cup, he didn't actually play any matches though, was just part of the squad, as he got injured in the warm-up before their second game.
Other than that Vassell won the FA Summer Tournament, Steve H**** won the Rous Cup and numerous Villa players won the Home International Championship, most recently Cowans and Withe in 1983 unless we had any Ulstermen that I've forgotten the season after.
Kieran Clarke and Richard Dunn won the Celtic Nations Cup, I think. They played in the opening group games in February 2011 but the final games weren't until the following May. I assume they got medals though.
Dwight Yorke won the Caribbean Cup on 9th July 1989 but I don't know if he'd actually signed for us yet.
I'm sure our players have probably won a fair few other minor tournaments, too.