I've always liked and sympathized with the Buffalo Bills who were the AFL champions in 1964 and 1965 the last two pre-Super Bowl years. And of course the Bills had the legendary Cookie Gilchrist at RB from 1962-64.
Of course there's a lot of good things that can be said about the Kansas City Chiefs as well, e.g. their bright and striking uniforms, their cool arrowhead logo, their participation in Super Bowl I and their subsequent victory in Super Bowl IV. Plus this video:
Snickers Chefs Commercial