Bushido Blade needs to return. It was a fighting game that actually felt like it was trying to be realistic. My friend and I played the heck out of it.
Likewise, I'd love to see another Way of the Samurai but with a far better budget. The branching path style was awesome.
SSX Tricky was my favorite game in the series by far. Tons of games have had "snowboard down the mountain" as the main theme but Tricky was different.
It's not the game listed in the OP but I'd kill for another Might & Magic: Clash of Heroes. Loved that game to death. I've probably beat it half a dozen times.
It's not a genre itself but I really liked the multiple protagonist setup for Suikoden 3. It was a fantastic idea for a game.