I actually like the Conway Twitty gags only because I'm a big fan of Conway Twitty. Not that I find them funny, it's that I just love the fact that 99% of the people who watch the show have no clue who Conway Twitty is and it DOES make me wonder how that affected sales of his music.
My problem with it is that it started as a reference to Hee Haw, completely in context. I forget exactly what episode it was, but they used it twice. Then, they had to run it into the ground, culminating in the worst one, an
entire song. Of course, that was part of the worst episode (the O.J. Simpson one that was poorly done all over). What I liked about Family Guy
was that it was snappy and random. And random doesn't mean doing the same gag over and over and over, making it more awkward and long every time. I do like the Chicken fights (Seth's not a huge fan of those either) for the action... but I actually miss the "This is worse than [80's reference/Star Wars Reference/Muppet Reference]" short bits.
Luckily, the show's starting to move away from that sort of thing and just focus on plots.