Support *moves* are kind of tricky to define, but things like Spore and Encore can give opportunity to a Pokemon's teammates (you switch in with a set-up sweeper or hazard setter to abuse the turns the opponent has to waste), so they'd be supportive. Passing stats with Baton Pass is supportive. Hazard setting (or hazard removal!) is supportive, as is passing large Wishes from the likes of Chansey or Alomomommymola. Depending on the team, U-turns and Volt Switches can be supportive (a lot of Pokemon REALLY appreciate a slow switch move. Reason is as follows.)
Opponent has a strong pokemon, like Garchomp.
You have a fast Pokemon with U-turn that can't really threaten Garchomp.
You use U-turn!
(Switch to Weavile, who can take out Garchomp.)
Garchomp uses Earthquake on Weavile!
Weavile is sad. ;_;
Alternatively:
Opponent has Garchomp
You have a slow Pokemon with U-turn that can't threaten Garchomp
Garchomp uses Earthquake!
Your slow, bulky Pokemon tanks the hit.
You use U-turn!
You switch to Weavile.
Weavile is now facing Garchomp on equal footing and can KO next turn :)
(that also kind of shows the difference between a check and a counter, as has been said. If Weavile was much much bulkier, it could switch in to any of Garchomp's moves without help and KO it. But it can't, it can only do it when it is in battle without taking an attack.)
Supportive Pokemon would be a bigger deal than supportive moves, IMO. Even support Pokemon run offensive moves, lest they be tauntbait (e.g. Skarmory and Brave Bird).
EDIT: 3x Shedinja/Ninjask/Greninja'd combo!!!