about the Avatar State...now that I look back upon the episodes where it has been triggered, it is caused by loss, potential or real. Here are my examples
1. Boy In the Iceberg. Avatar State seen to keep Aang alive in iceberg. This is the first few opening minutes, and it keeps the Avatar from losing his life. It is also possible that the Spirit helped keep the world from losing the Avatar all together, because the Air Nomad genocide happens soon after Aang runs away.
2. The Avatar Returns. Aang uses the Avatar State to create the tornado of water. Now some people may think that it was because he was in dire danger. That is probably only the tip of the iceberg. This danger almost caused Aang to lose his life; the end of the Avatar cycle, or at least a fully realized Avatar. Also, Katara is scared that she lost Aang in this moment, which is why she called out his name several times, right before the Spirit is activated.
3. The Southern Air Temple. Aang goes into the Avatar State once finding Monk Gyatso's corpse. Gyatso was a major part of Aang's childhood, and he was, according to Aang, the best airbender alive. This is basically when the belief that the airbenders may have survived comes crashing down on Aang, as well as probably his entire world. Loss of this magnitude causes him to snap and go into blind grief, triggering the Spirit.
4. The Spirit World (Winter Solstice Pt. 1). Not sure if this counts as his Spirit being triggered, but I will count the times when he crosses into the Spirit World. Sokka tries to help Aang, but is taken away by the Hei Bai Spirit. Aang attempts to save him, but is unable to reach Sokka before Hei Bai goes back into the Spirit World. In an attempt to help find and save him, Aang journeys into the Spirit World, trying to find answers. This ends up leading him to where he can contact Avatar Roku for guidance. In a roundabout way, he eventually saves Sokka by figuring out why the Spirit is attacking through his Avatar Spirit, especially when he sees he is sitting in front of a statue of the Hei Bai Spirit.
5. Avatar Roku (Winter Solstice Pt. 2). Aang, in the Avatar Spirit, is able to channel Avatar Roku's spirit and knowledge to defeat the threat of the Fire Nation firebenders. Aang, as well as Shiu (sp?) and his friends, are in danger of death/capture and torture. Potential loss of life and friends (I believe Aang befriended the Fire Sage by this point) was enough to trigger the Spirit.
6. The Storm. The first time is a brief second, when Aang is ranting about how he lost his friends, and then the head monk wanted to take away Gyatso. "They wanted to take away everyone I knew and everyone I love!" Aang screamed. Fortunately, Katara was able to calm him out of it and deal with Aang's personal little demons. Then we see him trigger the Avatar State, once again because of endangerment of losing his own life, as well as Sokka's, Katara's, Appa, and the fisherman dude.
7. Siege of the North (Pt. 1 and 2). Aang uses his Avatar Spirit to cross into the Spirit World in order to find the Ocean and Moon Spirits (Tui and La, push and pull, yin and yang, etc etc.) He goes in order to try and find a way for the Water Tribe to survive the Fire Nation invasion; otherwise, the Water Tribe would be entirely eradicated. When the Moon Spirit is gone, Aang triggers the Avatar Spirit, giving the koi fish, mortal form of the Ocean Spirit, to have bending capabilities and unleash its power due to imbalance. It is only when Yue decides to become the Moon Spirit and balance is restored does Aang's Avatar Spirit returns dormant.
8. The Avatar State. Aang goes berserk in the Avatar State when he feels that he was unable to save Katara, since the general fools him by sinking her into the ground. Believing he had lost Katara, he wreaked havoc upon the Earthbenders in the base.
9. Avatar Day. (I personally don't think the Avatar Spirit triggers in this one, but in case you think it does, I will put it in the examples.) Kyoshi comes to clarify some issues due to the loss of Qin the Conqueror. On a side note: those people were so daft even 2 year olds could have a better government!
10. The Desert. Aang has lost Appa already, which leaves him on the edge of going into the Avatar State, similar to why he goes into the Avatar State for Gyatso. When he hears that Appa was muzzled, the anger and grief he felt for the loss of his friend as well as the injustice just tips him over the scale; the loss of Appa finally wears him down and the Avatar State is released.
So that pretty much is what I think about that, seeing how the season finale is focused around the Avatar State. So basically in a nutshell: There are major parts in Aang's world. Loss of any will cause so much pain that it will send him into the Avatar State, so you better run if you caused him that much pain.