One vs Many board games
One vs. Many is a fairly recent term concerning boardgames.  There aren't any dedicated lists on Boardgamegeek that I was able to find.  However, there is a tag by that name that you can use to find games.
Also, see the list of One Vs. Many games in a GeekList devoted to Cooperative games.
Cooperative Games
Cooperative games are also a type of game you may wish to consider.  It has become very popular in recent years.  Instead of contesting with each other, the players work together to beat &quot;the game&quot;.  In many ways, the game system acts as the GM against the players.  The above list is very thorough if you want to see some examples.
Traitor Mechanic
Another related term to look for is boardgames with a Traitor mechanic. A game with a traitor is cooperative except for usually one traitor who works against everyone else.  However the identity of the traitor is not usually initially known.  These sorts of games can be a lot of fun if your group enjoys playing mental tricks on each other.  A geeklist, of games with a hidden traitor mechanic can be helpful in locating those.