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Haha sadly I feel the same way about the trophy system. Buying the vita brought out this weird need in me to collect trophies. Motorstorm rc also has trophies and is free, but these are the only 2 currently. As far as I know there are no plans to give trophies for the free ar games, and I don't know of any other free games.
The coolest things about Motorstorm RC is that it has a platinum trophy, and if you buy the PS3 version of Motorstorm RC, any trophy you earn on the Vita also pops up on the PS3 version. 2 full sets of trophies for $10. Not a bad deal.