(1) Peter Griffin
Peter is the head of the family, and if you are looking for those good old fashioned family values, then you won't find them here. Often the character featured most in the show, his bizarre exploits over the episodes are impossible to keep tabs on. There are various running themes with his character, often referring back to when he had a certain experience or did something completely implausible.
(2) Lois Griffin
The husband of Peter, a slightly lesser character in terms of time featured which often involves the result of Peter's activities with her as the long suffering wife. Some episodes do however essentially follow her character completely.
(3) Chris Griffin
The lazy and fat son of the Griffins he is not particularly popular at school (which periodically changes in particular episodes). Portrayed as generally slow on the uptake, his character probably develops the least in the shows.
(4) Meg Griffin
The people behind the show obviously decided it would be good to have a character that everyone hates unfairly, and that character is Meg! The rest of the family dislike her and are almost ashamed of her, although Lois sometimes appears caring towards her and helping her out with her problems in general she is not treated equally to the rest of the family.
(5) Stewie Griffin
The psychotic baby that is bent on revenge against Lois for being born. Probably the second most important character after Peter, many episodes feature Stewie prominently and his scheming. Some people can hear him talking, others can't - all very amusing, and he gets a lot of the good lines in the show.
(6) Brian
The pet dog, Brian of course can talk, and is a friend to everyone. Often his escapades with Stewie or Peter are following in an episode to humorous effect with various dog related jokes.
(7) Quagmire
Glenn Quagmire is the neighbour of the Griffins and features in many episodes either to a greater or lesser extent. He has one big obsession and this is usually mentioned whenever he is in the show.
(8) Cleveland Brown
Another friend of Peter, Cleveland is often featured in scenes at the bar and generally in episodes. Now has his own show, the Cleveland show, which is interesting as several of the other lesser characters looked like more promising ones for character development and their own show.
(9) Joe Swanson
The paraplegic police officer that is part of Peter's gang of four, along with Quagmire and Cleveland. He is surprisingly athletic but also prone to sudden extreme anger.