Family Guy was amazing to watch from the whole of season 1 to the first few episodes of the 4th season. This is mainly due to the fact that all the characters used to be actually good. Lois used to be a caring and true mother who didn't have the awkward laugh at cringed people, Meg was treated normally and was the normal stereotypical girl everyone likes, Brian actually wasn't the greedy dog who tries to be someone who he isn't and gave actually good advice to other characters, and Quagmire was the sex-addict who didn't hate on Brian. Plus they draw out many of the fan jokes that were really funny from the first few seasons.
All the other characters have suffered over the years as well. So, if you choose to watch Family Guy, I highly recommend that you watch the first few seasons first, because you will easily see the comparison between the early on episodes with the present and you will truly admire each character. By the way, the cutaway scenes are really funny! I say this show is overall the best show I've ever watched to date.