I remember seeing early promos for American Dad on Adult Swim, to be honest, it didn't look special. And it's pilot...well it wasn't still. American Dad has always had to live in the shadow of its older brother, Family Guy. And much like being the younger child trying to achieve their place in the world in the shadow of an over-achieving older sibling, American Dad had to find it's own way into the animated sitcom world, and do it on it's own terms.
One thing that American Dad (we'll just call it AD for short) strives to set itself apart is to do away with the scatter-brain comedy of Family Guy, namely, the cutaway gags. There are none to be had here, except maybe sort of one in the pilot. Instead each episode tends to follow a main story, usually Stan learning something by episode's end, and a side story involving another member of the Smith Family. This allows for more structured story-telling and a chance to really dig into the characters. Stan even follows a notable change throughout the series, namely his views on homosexuality. In the beginning of the series he can't stand the idea of two men being together, and now he has little to no issues with Greg and Terry.
I'd love to describe the Smith Family in depth but, I don't have the word space to do so, nor would it be appropriate for a review to tell you absolutely EVERYTHING about it. From this troper's point of view, this cast as far and away stronger than Family Guy's and The Cleveland Show. Characters are colorful (both aesthetically and figuratively) it's hard to say enough about them, but there are not too many that are just throwaways, as much of AD follows a nice continuity. If something changes in the cast, you can almost bet the consequence of such an event will be mentioned later.
Ultimately, I leave you with this: Give this show a chance. If you saw it before and thought it was crap, it might have been when it started out. But it's come a long way, made a name for itself and is a much stronger show for abandoning Family Guy's random antics. The show may seem to promote Republican values, but it honestly mocks it as it praises it. It's easily one of my favorite series on TV, and I hope it goes strong for awhile. It's got some risky writing, it's creative, and most of all it's funny. Give it a shot, you might be surprised.