"What is the most broken game that you tried and loved to play, warts and all?"
Well, because I shat all over D&D yesterday, I may as well give some good memories of the early D&D Next Playtest; specifically the first release. Things were unbalanced, and not necessarily worded correctly, but the feel was classic, and that may have contributed to my enjoyment.
Those that remember, as it was really only a couple years ago now, when Wizards announced they were going to be completely open with the next iteration of D&D, inviting beta testers to take the game through its beginning hurdles to something releasable. The first playtest release for the game had the four core races (Human, Elf, Dwarf, Halfling), as well as the four core classes (Fighter, Wizard, Rogue, Cleric). It was iconic, and super basic, and filled with the possibilities of a genre renaissance.
What I remember most about the ruleset wasn't necessarily how certain parts of the release didn't really mesh with others, or that certain classes were hideously overpowered; rather, I remember that instead of getting tied up with rules lawyering, the group I played with just sort of had fun with the setting, using character sheets and rules as very loose guidelines for play.
We traversed through the Caves of Chaos, fought kobolds, an owlbear, and human death cultists, somehow found our way into a nuclear silo, and our wizard detonated it...somehow? I think resonances were involved, or something. Regardless, it was pulpy, and fun, and fast paced, and I couldn't wait to run my own game in it, which turned out to be super easy and fun.
And then they kept releasing stuff, and I got less excited. Man this story is getting depressing.