As it stands now, I'd say that Clemson and Bama are clearly the best teams of this era.
Then you can argue between Oklahoma and Ohio State. I think they are pretty close, as Ohio State does have a title and better record, but Oklahoma has more playoff appearances. Although Oklahoma has lost all of their games, they were competitive and really let that game against Georgia slip away.
Then like you mentioned teams that have at least won a game, though only appeared once each I believe, you have Oregon and Georgia.
Another interesting tidbit, appearances by conference:
SEC: Alabama: 5, Georgia: 1, LSU: 1, Total: 7
ACC: Clemson: 5, Florida State: 1, Total: 6
Big Ten: Ohio State: 3, Michigan State: 1, Total: 4
Big XII: Oklahoma: 4, Total: 4
Pac 12: Oregon: 1, Washington: 1, Total: 2
Independent: Notre Dame: 1, Total: 1