The story, art, and sound in this anime are good-average, however the characters and their developments throughout the story are excellent.
The characters are believable, memorable, and have meaningful interactions. Since the scenario and characters seem so real Clannad pulls on a lot of emotions, joy and sadness are common enough in anime but this one managed to get some despair and rage out of me too.
It's certainly not all fun and games, but Clannad: After Story is worth a watch in my book.
If you have extra time, watching Clannad beforehand might be good, but I don't think its necessary.