Okay, so far the minis program has been, well, something of a bust, at least for me. We're seeing mostly puzzle games, TD games (not all minis, but 4 since the PSPGo launched) and some basic action games.
On the other hand, the iPhone (which the Minis or pseudo-Minis often come from) seems to have all sorts of games, which is more what I was expecting.
I guess some of this is those games are easier to make/port (though the one really original Mini, Zombie Tycoon, seems to be pretty complex and it came out quickly).
Anyway, what I'd personally like (and hope) to see (and think would work well in the minis format):
Vertical shooters - Galaga, Space Invaders, Gorf, Galaxian, Phoenix, etc. These are really one of my favorite types of games, period, I still have a 2600 hooked up to my TV so I can play Phoenix and Space Invaders. (There don't seem to be any in the works)
RPGs - this might sound too ambitious, but the iPhone has several. Some old school (like Wizardry or Bard's Tale), some action rpgs, even a Wolfentstein RPG. (One involving steampunk cats is supposedly coming next year)
Strategy games - Non TD ones. Advance Wars clones would be nice, the iPhone also has Archon (and an updated version), even basically the DS port of Civilization Revolution ($30 on DS, $5 on iphone, boo)
Horizontal Shooters - Not so much like the R-Type, but something more akin to the old school ones. Scramble, Super Cobra, Cosmic Avenger (my favorite on the Colecovision), Vanguard (favorite on the 2600), Looping, Choplifter, Fort Apocalypse (like Choplifter on steroids), etc. (There does seem to be one R-Type sort of shooter in the works and maybe a Chopper Command clone)
FPSes - while the PSP is perhaps not the best for a modern FPS (where you aim up and down), the older ones like Doom or Wolfenstein would work pretty good. (None in the works?)
Card Games - Solitaire and Canasta would be my picks. My favorite GBA cart was Ultimate Card Games and there really isn't a PSP equivalent (there is World Championship Cards, but it's awful, they just took their poker engine and stuck in other card games. How do you play canasta on a poker table? Ick). (A Texas Hold'em Game from EA is coming)