While you may not control them directly, you can assign them to different dungeons, towns, or whatever. Just grab a window and drag it to a new zone and the character will teleport to the new zone and do his dungeon crawling thing.
Each character type may have different priorities or may react differently to meeting one of the other characters in a dungeon. For instance, a monster really just wants to be strong - so it won't take any treasure or explore. It will just look for combat and try to grow stronger. However, a Merchant character may explore the dungeons and avoid combat in favor of raiding treasure chests of loot he can sell in town. If the Merchant character were to meet an Elven Archer character, they may decide to engage in a trade for goods (the Merchant has a really nice bow the Archer could really use) - but if the Merchant meets that skeleton, there's fighting to be had.
The different areas are not always dungeons either, though a large part of it will be. There might be something like an arena, where any character you drop onto it will fight in arena games for money. A training facility where dropped units do weight lifting to improve strength, a library where they read books to improve intelligence, and so on. In a flea market, a character may try to sell his wares to other characters. And so on.
So, rather than being a game with a specific goal, it's more a sort of simulation game where you just watch entities interact. However, you have some control over it. By moving units togheter in unique ways, you can greatly influence a game. For instance, purposely putting a human in a zone with a werewolf could yield two werewolfs, or perhaps drop some piggy animals in the zone to feed it. Putting different characters together in controlled (and uncontrolled) situations can yield interesting results.
I really think there should be a major exploration aspect to this idea. For instance, if you start with a regular human character, depending on how his stats are built up, he may class change into a warrior or a wizard - and depending on what experiences he's had, he may become a paladin or a death knight. There could even be a crafting element where loot found in particular dungeons can be used to build town facilities or something. There should be dozens of different character classes, all interacting with each other in unique ways. So it should be done in such a way that the player is constantly "unlocking" new characters and zones and they can't wait to see what happens when you mix A with B.
Then, you just stick it in a window while you surf the internet or something, keeping an eye on them in the watch window, and every once in a while, moving them around to new areas.