At the end of series 3, you never really find out what happens to Zuko's Mom, do you? well, I've got an idea, check this out:

Ozai wanted to be firelord, but Azulon wouldn't let him be next in line, yadda yadda yadda, Iroh and Lu Ten, yadda yadda yadda, Ozai has to kill his first born son. But Ursa didn't like that so she planned a plan so that Ozai would be firelord and Zuko would live, but then Ursa was banished and I THINK that Ozai killed Azulon but who knows. So, Ursa is banished, and I don't really know where she's gone....but remember when Aang was in the spirit world and he had to talk to "The Face Stealer" (Can't remember the name-sorry) and he changes his face, Right? Well you know that face or a girl with long dark hair? Doen't she look alot like Ursa? If you don't think so just have a look at how different Azula looked when she was crazy and cut her hair.

Think about it...I could be right!

So she got trapped in the spirit world