Sim Hero Classic is an RPG/Simulation game where you manage groups of adventurers & send them into dungeons. This game can be thought of as a cross between an 8-bit CRPG & a typical sports-sim. Sim Hero is the most feature-rich rpg management sim that exists in the world... no, really! Oh, and it's FREE!
Each battle isn't controllable (there are TONS of JRPGs out there if you want to control the battle), but you can comb thru the battlelogs to see how your heroes fared!