These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Archive Panic - While 14 studio albums may not seem much, they're often over 70 minutes. Also, she has over 30 official bootlegs, and lots and lots of b-sides and covers. Good luck.
Awesome Music - The long 'girrrrrrrrrrrrrrrrrrrrrrrl' in live performances of "Precious Things".
Toriphiles & ex-Toriphiles can agree that her first five albums and Scarlet's Walk fall under this trope. A devoted Toriphile would say that virtually everything she has done is this.
Broken Base - Tori's fanbase can be summed up as 1/2 devoted fans and 1/2 ex-fans who complain too much that Tori's not making depressing piano music anymore.
Crazy Awesome - She's quite awesome, and quite mad, and these are codependent traits; She dresses up as different personas and plays two pianos while straddling the bench. She speaks of fairies and making love to 'the Wolf' in interviews. Delirium of Neil Gaiman's The Sandman is partially based on her in later volumes, though in the beginning she just happened to resemble the Anthropomorphic Personification of Crazy Awesome.
Ear Worm - Toriphiles tend to get a lot of her songs stuck in their heads.
Ensemble Dark Horse - Many of her B-sides are very popular with Toriphiles, especially "Cooling", "Sugar", and "Honey". "Cooling" even topped a poll of greatest Tori Amos songs. In other words, "Cooling" got more votes than all of Tori's other songs on this poll.
Epic Riff - "Professional Widow" (harpsichord), "Precious Things" (piano), and "Silent All These Years" (also piano).
Misattributed Song - No, "Kissing in the Rain" on the soundtrack for Great Expectations is neither written nor sung by Tori, though she did contribute to other songs in the film. This track is written by Patrick Doyle with vocals by Miriam Stockley.
Signature Song - "Cornflake Girl" is what the general public remembers her for.
Squick - What some people think her song "Raspberry Swirl" is about: having sex with a woman on her period. The "raspberry swirl" is a mixture of menstrual blood and semen. Although Tori confirmed that the song is about how she always got her friends' backs, but she probably invoked such imagery on purpose.
Surprisingly Improved Sequel - Y Kant Tori Read infamously flopped, and Tori's solo debut Little Earthquakes became a success. Some may say that Under the Pink is even better than Little Earthquakes.
They Changed It, Now It Sucks - What many fans thought about her 2005 - 2009 material. It's been joked amongst some fans that the quality of her music is directly tied to how angry Tori is, and she has mellowed out ever since the birth of her daughter.