The AoO for standing up, like all AoOs, disrupts and occurs before the action that provoked it is completed. This is the same reason if someone charges you when you have a reach trip weapon, they go prone in the sqaure they were about to exit that you threatened -- and thus can't close the distance with you and still take their melee attack with the prone penalty. Therefore, you cannot trip someone on the AoO for standing, as they have not stood up yet.
This was a change from 3.0 where you COULD do what people are talking about, and the change was completely intentional. I still remember it was different in 3.0 because of one battle where the psion, untrained in tripping and fairly weak, but buffed to the gills with AC so as to not fear provoking himself, had nothing better to do and decided to just try tripping the BBEG. He rolled amazingly well. Repeatedly. And due to how 3.0 did things, much to even his surprise, he could just keep chain tripping him as he tried to stand, and the BBEG spent the entire rest of the fight on his back, never being able to stand.
"An attack of opportunity "interrupts" the normal flow of actions in the round. If an attack of opportunity is provoked, immediately resolve the attack of opportunity, then continue with the next character’s turn (or complete the current turn, if the attack of opportunity was provoked in the midst of a character’s turn)."
Maybe it's a house rule I'm remembering, but I thought it was only possible to make 1 AoO against a single opponent each combat round regardless of how many times they provoke one. It avoids precisely this sort of shenanigan.
Attacks Of Opportunity :: d20srd.org
"Combat Reflexes and Additional Attacks of Opportunity
If you have the Combat Reflexes feat you can add your Dexterity modifier to the number of attacks of opportunity you can make in a round. This feat does not let you make more than one attack for a given opportunity, but if the same opponent provokes two attacks of opportunity from you, you could make two separate attacks of opportunity (since each one represents a different opportunity). Moving out of more than one square threatened by the same opponent in the same round doesn’t count as more than one opportunity for that opponent. All these attacks are at your full normal attack bonus."