What is the most broken game that you tried and loved to play, warts and all?
My initial knee-jerk answer to this was any game by Palladium, but then I gave it some thought. For all the guff it receives, I wouldn't call Palladium's core system "broken," necessarily. Creaky as hell? Yes. Non-intuitive? Absolutely. And it's those elements that killed our enthusiasm for Palladium rather than any perceptions of brokenness.
Of course, Rifts is a whole other ball of wax, potentially. But even then, I think the most broken system that got played warts-and-all anyway had to have been AD&D 2.5. That is to say, Second Edition circa the mid-90s, back when there were a ton of splats and (even worse) the Player's Option series. I've written before about those dark days, when TSR was churning out unplaytested material by the ream, and that's not even counting the stuff that showed up in Dragon magazine every month. My memories of games played back then are full of just flat-out game-breaking characters.
But we still had fun with it. Some of our most successful AD&D campaigns of that era hail from the 2.5e years. There's no doubt that by the time Third Edition came out, we were all ready for it, and welcomed it with open arms, but I think there's something to be said that, up until August of 2000, we were still chugging along with our "broken" AD&D games.
The funny denouement to all this is that I've recently come back to running 2e. I've played a bunch of retro-clones and neo-clones over the last five years or so, but so far this 2e campaign is the most fun I've had playing traditional D&D. I'm sure part of that is simple familiarity - 2e is by far the edition I've run the most of - but I have to say that I'm also enjoying the "warts and all" nature of this particular edition. It hits a nice sweet spot in terms of organization and explication versus funky old school mechanics that allow for rulings over rules. Pretty much all the house rules we're using right now come out of personal preferences rather than any attempt to "fix" the system.
That said, I'm exercising quite a bit of DM oversight in terms of what I'm allowing in my campaign, and I have zero interest in returning full-on to the days of Player's Option and edition 2.5.