Kaeoschassis: Most of mine have already been mentioned I think, but for me it's invariably the "sort-of-failed-experiments". Those games that tried something different, shot way, way higher than they could actually hit, and ended up as... well, broken, buggy, choppy messes, to be honest. But sometimes the great ideas and the effort are so amazing that they shine through any number of bugs - and of course there are usually modding communities more than willing to pick up where the devs had to leave off.
Not just games that were released buggy or unfinished, either. Games that were genuinely great, but failed commercially also come under that "failed experiment" category. Maybe they were poorly marketed, maybe they just had the misfortune of going up against another more popular title.
Let me think...
Vampire Bloodlines - broken and buggy practically to the point of being unplayable on release, and since the devs went bust creating it, still requires a bunch of modding and tweaking to get it up to scratch. But what a vision. There will never be anything else quite like it.
Every Stalker game - haven't actually played CoP yet, but the other two definitely qualify. They're broken to a hilarious degree, but just so fun. They are so atypical of shooters in practically every way, and even if the devs missed the target they were aiming for by miles, they tried, and we got an amazing experience as a result.
Terra Nova: Strike Force Centauri - let's talk classics here. Looking Glass are legends, and rightly so. Thief and System shock are both titles that have such, such special places in my heart - in Thief's case, it's probably more deserving of that place than TN is. But they get all the love. Terra Nova was a commercial failure and has faded so far into obscurity that I don't think there's anywhere that legally sells it right now - and no, incase you're wondering, I don't have a working copy anymore. But it deserved to shine. Interesting plot, compelling and then-unheard of gameplay, and technical achievements that put it way, way ahead of its time - Terra Nova was a triumph in every way except sales, and there are elements of its gameplay that have still never been matched or bettered.
I'll almost certainly be adding to this list when I'm less sleepy. I get pretty passionate when it comes to those 'flawed' classics.
With the absolute busted and mile away mark it hit you know you have something special when it is still something awesome. Reminds me alot of KOTOR 2 in that regard. Practically broken and held together with glue and staples it was still lauded. Art through adversity.