I still look for series that aren't finished to explore. I had read the asoiaf series and I was fine with where it ended in the books. I guess it could be because I still had the show to look forward to at the time.

I've finished lots of manga where the ending was bad or there's no real progression of plot, that's sort of like unfinished types to me. Like the Rozen Maiden manga, original 1-8, they don't have an ending to the arc, where the Anime actually completes the story. Comedy stuff is more of an experience too so I can handle if it ends upruptly.