Munchkin as a two player game
As Matt Sheppard notes, the main problem with two-player Munchkin is that it eliminates the automatic balancing effect present with three or more players, where the weaker players can band together to pull the stronger ones down.  In normal play, this is the main effect that counteracts the otherwise fundamental unfairness of Munchkin &mdash; without it, it's quite possible for the game to quickly get so unbalanced that one of the players is almost sure to win no matter what the other does.

This can be a problem especially if one of the players is new to the game: if the experienced player plays for keeps, they're likely to leave the newbie feeling like they didn't even have a chance, whereas if they pull their punches, the game is likely to get boring because there won't any of the scheming and backstabbing that makes normal Munchkin interesting.

That said, I do think that Munchkin with two players can potentially be fun, provided that both players are a) about equally skilled, b) reasonably familiar with the game and how it's typically played, and c) aware that they're playing the game in a way it was not designed for.  In particular, it's probably a good idea for both players to be experienced enough to tell when they're in a hopeless situation, so that they can either concede the game or just play it out quickly and get on with the next round.

As for house rules, I have no real experience to share.  However, one possibility I'd strongly suggest would be going over the deck and picking out some of the most egregiously unbalanced cards like the Kneepads of Allure.  Basically, if it feels unbalanced in a multiplayer game, it's likely to be even more so with only two players.  Also, if the players are not quite perfectly matched, some kind of handicap system, such as extra starting levels, might be useful to compensate for the lack of automatic balancing.



Ps. From a game theoretical perspective, two-player Munchkin ought to be pretty dull: it's a two-player zero sum game, where the success of one player (measured as expected probability of eventually winning) is exactly the complement of that of the other.  Thus, in optimal play, there really shouldn't be any (unforced) helping or trading, or anything else that requires the consent of both players.

The reason it can still work out in practice is that real humans are not the perfectly rational, risk-neutral and infinitely patient and foresightful agents assumed in classical game theory.  Thus, in a real game it can happen that, say, both players find that trading certain items puts them both in more comfortable positions, or that one player is willing to accept a reward for helping that the other is willing to offer.

Also, the strategic elements of Munchkin are not entirely based on cooperation and trading: besides the simple process of optimizing your character build, there's quite a bit of strategy involved in deciding when to spend your one-shot cards and when to save them.  That still applies even in a two-player game.