Yeah, I love playing PSP games on the Vita. In fact, I've spent more money on PSP games than Vita ones since I got it! I bought HSG ($30) and Wipeout ($40-20=$20) with a bonus $20 gift card, so $50 on Vita games.
For PSP games, I bought:
Tactics Ogre: LUCT ($20)
Valkyria Chronicles II + DLC ($22.50)
Street Fighter Alpha 3 MAX ($10)
Legend of Heroes: Trails in the Sky ($20)
PSP total: $72.50
And I'm STILL excited to eventually play Darkstalkers, Ys Seven, Ys: Oath in Felghana, Half Minute Hero, Lunar: Silver Star Harmony, Dissidia 012: Duodecim, Corpse Party, Disgaea 1, 2+3, Z.H.P., Ultimate Ghosts 'N Goblins, Mega Man: Maverick Hunter X, Prinny 1+2, Person 1, 2+3, Guilty Gear XX Accent Core Plus, God of War: Chains of Olympus, God of War: Ghost of Sparta, and maybe Cladun 1+2. And this is just what's on the Vita store right now!
It's pretty much like the Vita launched with a ton of great games, because the experience on the Vita is so vastly superior to the one on the PSP.
I must say, though, that buying Tactics Ogre and VCII at the same time may have been a mistake. They're both awesome, obviously, but having two very-long SRPGs at once is pretty daunting, haha. It's often hard to choose which to play!