The only thing I have to add to the other reviews is that this title is emotionally intense, in spite of the quirky lightness that pops up from time to time.
Where Clannad lifted your spirits and made you happy, After Story waits for you to care deeply about all the characters, then put them through horrible situations, then make you think things are looking up, only to pull the rug out from under you and stomp on your heart again.
Wishes and despair feature heavily in this show.

I'm with ABlipinTime, this series is hard to rate in terms of content. While the objectionable stuff is there, it's completely necessary to the plot and is handled maturely.

Violence/Gore - Some. Brutal fistfights involving gangs at the most.

Nudity/Sexual Content - Nearly nothing. The topic of sex is discussed, but not in an inappropriate way.

Theo. Themes - The strange robot and girl in the dream-ish world from Clannad continue to appear.

Other Themes - One scene of drug use. One character is an alcoholic. Some smoking. Some swearing.

If you haven't seen Clannad, you really need to watch it to understand what's going on in this story. The quality of this anime is pretty much the same as before.

It's hard to rate this anime on certain things. For example, while there is violence, it may not appear relevant to the plot (it is), but it isn't always unbearable to watch either (no blood spilling, but there are obvious and sometimes serious injuries).

Nudity and sexual content are hard to rate since they aren't as prominent as you might think based on the ratings.
Spoiler: There is discussion of the main characters having sex to have a child, but it is never actually shown.

The story revolves around the events of the first one, so there is some mysticism, but it's primarily a plot device used for discussion and alittle deus ex machina.