OK, here we go!
Snow White
-The first Disney Princess ever created (Obviously...)
-The first Disney Princess with black hair
-The first princess born into royalty through parents
-The first princess we see with both parents deceased
-The first princess we see being raised by an evil step parent
-The first and ONLY princess to have received assistance from dwarfs (or I should say, she gave THEM assistance

-The only princess with a voice so high only dogs could hear her

-The first princess to have ever graced the screen in song
-The first princess seen in a chambermaid/commoner's outfit
-The first princess to have been revived through love's first kiss
-The first princess whose villain changed forms in other to accomplish her goal
-The first princess to have a duet with her prince (though would later sing all of the film's songs by herself)
-The first princess to receive an Academy Award (though it was an honorary award)
Cinderella
-The first blond princess
-The first princess NOT born into royalty
-Though not royalty she is the first commoner born into wealth (though her story before the Tremaines stepped in is unknown it is implied that her original family was wealthy, and that Lady Tremaine married Cinderella's family for his wealth)
-The only princess with step sisters (or siblings for that matter)
-The first princess to have received magical assistance (thanks to the Fairy Godmother)
-The only princess to have revived her past thanks to Lady Tremaine changing the course of history in Cinderella III
-The first princess to have animal friends that talk to her (though only the mice talk to her)
-The first princess to have her dress destroyed on screen
-The first princess to have a pet (It is assumed that she had Bruno the dog long before the Tremaines and their cat Lucifer stepped in)
-The first princess with a horse (though she never rode it till the third film)
Princess Aurora (Sleeping Beauty)
-The first and only princess to have both parents living at the beginning and end of the story
-The second princess born into royalty
-The only princess with a death spell placed upon her at birth
-The only princess to have been raised by fairies
-The first princess to have remained silence throughout most of her picture (though she is the only princess to never say a line after her introduction and before the ending)
-The second blond princess
-The first princess whose prince fought the villain head on (neither did The Prince and Prince Charming face his princess's antagonist at the end of their respective film)
-The only princess whose villain turned into a dragon (though not the first villain to turn into an alternate form)
-The only princess whose main outfit has alternate colors
-The only princess born into royalty, but raised as a commoner
-The first princess to receive an attraction at one of the Disney theme parks (Sleeping Beauty's castle was created before the release of the film)
Ariel, The Little Mermaid
-The first red headed princess
-The first princess who is NOT a human
-The only princess whose fate at the end of the film is drastically different from the original story (in the original, the mermaid dies and turns into sea foam)
-The only princess to have become a mother
-The second princess to be mute throughout most of the movie (Aurora was the first, but Ariel's was due to a magic spell)
-We know how one of her relatives dies (her mother was crushed by a Pirate ship, as revealed in "Ariel's beginning")
-The first princess to receive a TV series
-The only princess to close Disney's DTV legacy (Ariel's Beginning is the last planned Disney DTV sequel)
Belle, Beauty and the Beast
-The first princess born a commoner
-The first princess whose living parent is not royalty or wealthy (her father is an inventor)
-The only princess whose only living relative is NOT evil
-The first princess to have a male antagonist (Gaston)
-The first brunette princess
-The first princess that doesn't sing her theme song (though she sings "Belle" and "Something there", the overall theme of the film is sung by Angela Landsbury)
-The first princess that becomes royalty through marriage
-The first princess whose story was turned into a Broadway play
-The only princess to have a Holiday themed special
-The first princess to have been romantically involved with a cursed prince
-The first princess considered an "outsider" by the village people
Jasmine, Aladdin
-The only princess who is not the focal point of the story (that honor belongs to Aladdin)
-The only princess to have tried to escape her royal duties
-The first non-Caucasian princess
-The only princess whose sole theme song is a duet with her prince (though Snow White, Cinderella and Aurora had duet songs, they also had their own songs. Jasmine didn't have a song in the original film)
-The first princess to have two actresses play her role (one talking, one singing. If I am not mistaken, all the actresses that played the princesses prior to Jasmine both sang and performed their roles)
-The only princess to have an exotic animal (a tiger) as a pet
-The second princess to receive a TV series
-The first princess to receive a DTV sequel
-The first princess romantically involved with a commoner (though Aladdin will become a prince, then a Sultan)
-The only princess to have crossed over to other Disney worlds (in the Hercules TV series she helps Aladdin and Hercules defeat a resurrected jafar)
Pocahontas
-The first American princess (Princess Maddy, from "The Princess and the Frog", will be the second)
-The first princess based on a real historical figure
-The first Native American Princess (though not a princess, but her position as the Chief's daughter puts her in a similar position)
-The only princess with two love interests (in the original film, she falls in love with John Smith, but in the second she marries John Rolfe. The second marriage is historically accurate)
-The first princess to have tried to prevent a war
-The first princess with a multiracial relationship
Mulan
-The first Asian princess
-The only princess who isn't really a princess (she was never a princess in the original story)
-The only princess to cross dress (she dressed as a man in order to prevent her father from going to war)
-The only princess to have brought disgrace to her kingdom (though her heroic efforts are celebrated in the end her acts are considered a crime)
-The second princess born into a commoner's life, BUT is the first commoner with both parents living when the story begins
-The only princess with a spiritual guardian (Mushu)
-The first princess to have done battle
Giselle
-The third princess born a commoner
-The ONLY princess to have crossed into the real world
-The ONLY princess to have 2D and live action counterparts
-The only princess who remained a commoner by the time the story ends (while Giselle was destined to marry Prince Edward, she goes with Robert instead)
-The only princess to decline a prince's marriage proposal (though she accepted at first, the events in the movie lead her to choose Robert)
That's all I can remember for all. If I missed something let me know.
I still have one fact missing; which the princesses has the oldest story (ie, which fairy tale has been around the longest).
If someone can answer that I'll greatly appreciate it.