D&D miniatures is designed to be an adversarial game (PVP). There may be some online supplements that expanded on the random dungeon bit presented in the miniatures handbook. It was a method for using the prepacked cards to sort of make random dungeons.
But in all fairness you can run a mindless dungeon crawl in any edition of any game. I am not sure of what your idea of "mindless" is. But there are some great "Megadungeon" types of products available for 2e and 3e D&D. (I am not sure, but I do not believe I have seen the mega dungeon resurface into the published realm in 4e). You could also grab standalone modules. But if modules are not your idea of fun there are other options.
Another option that my group does every once in a while when no one has anything prepared to run, is we get out the Dragon Compendium (the 3.x one, but you could easily use the charts to generate dungeons for any edition, or even any fantasy really) and use the random dungeon generation rules in it to make a random dungeon as we play it (we even take turns "rolling" up the rooms sometimes). Sometimes we end up with deathtraps, sometimes we end up with dead end dungeons, and every once in a while it churns out something really neat. But it is never the same dungeon, and it takes absolutley zero prep, and its fun for my group.
I am not sure what type of rule set you are looking for. But pretty much all flavors of D&D-ish games have some sort of random encounter generation. It can be as easy as grabbing some random map off of the internet (or making one on some graph paper, and filling up the rooms with random encounters. You could even chuck in a trap or two for good measure.
But the level of story elements you include are up to you.
I know this will sound like a bash (but in this case it is not), but if youa re just looking for good quick action, and the volume turned down on everything else, I reccomend D&D 4e. Most other rulesets have heavy leanings towards non-combat types of play (which makes it easy for a player to nerf their character during creation, if they select a lot of those abilities for a combat only game), or more simulationist types of play (which require more mastery). 4e on the other hand is largely invested in combat, is easy to pick up, and does not require very much mastery at all to get started (on either the part of the DM or the players). And the combat is fairly tactical, so it makes for a good "romp" system.
Another thing you may consider if you are looking for a pure combat experience, is a board game. There are some FABULOUS dungeon crawl boardgames out there. Hell, there are countless mods and downloadable scenarios for games like Heroquest, Descent, and even the old D&D boardgames. My group rocks those once every couple of months, and they are always fun, and typically have nothing to do with story (mostly about smashing monsters and living to do it again in the next room).
I hope you find what you are looking for.
love,
malkav