The Ninth Doctors we have seen are the Christopher Eccleston one, the Shalka Doctor, "The Curse of Fatal Death" Doctor, The War Doctor, the Doctor from "Party Animals" (Doctor Who Magazine comic story) (who is seen again in "Wormwood" (Doctor Who Magazine comic story)), unspecified ones from "The Gallifrey Chronicles" (novel) and "The Tomorrow Windows" (novel), and possibly the unspecified incarnations from "The Dalek Factor" (novel), "The Cabinet of Light" (novel), and "The Infinity Doctors" (novel).
The last Eighth Doctor Adventure "The Gallifrey Chronicles" (novel) states that the Doctor has three ninth incarnations, but it is never specified who/what these are.
The earlier Eighth Doctor Adventure "The Tomorrow Windows" (novel) has the Eighth Doctor looking into his future and seeing various future incarnations. These are the Rowan Atkinson Doctor from "The Curse of Fatal Death" , the Richard E. Grant Doctor from "Scream of the Shalka" (webcast), the redhaired Doctor from the Short Trip "Good Companions" (short story), a Doctor who sounds very much like William Hartnell in "An Unearthly Child", three other Doctors who are not recognised, and then what sounds like the Christopher Eccleston Doctor (from "Rose").
"Party Animals" (Doctor Who Magazine comic story) had the Seventh Doctor and Ace encountering a future version of the Doctor, who resembled Nicholas Briggs. In the later story, "Wormwood" (Doctor Who Magazine comic story) the Eighth Doctor and Izzy encounter a shapechanger which changes its appearance to resemble the Ninth Doctor. This is exactly the same as the future Doctor that the Seventh Doctor and Ace had encountered.
The Telos Novella "The Cabinet of Light" (novel) has a Doctor who does not resemble any television version, nor any of the others listed here. But it is unclear if this is meant to be a Ninth Doctor, a future incarnation, or a Doctor from any continuity entirely.
The Telos Novella "The Dalek Factor" (novel) has a Doctor during the Time War. Fans have argued over whether this is the Paul McGann Doctor or the Christopher Eccleston Doctor. He wears a leather coat. However it may be neither...
In the television episode "The Name of the Doctor", we meet a previously unheard incarnation of the Doctor, played by John Hurt. He is revealed in "The Day of the Doctor" to be the 9th incarnation of the Doctor, but since he does not go by the name "Doctor", he isn't counted in the numbering, and is referred to officially out of universe as the War Doctor. He resembles the Doctor described in "The Dalek Factor" (novel). The Doctor in "The Infinity Doctors" (novel) is unspecified, and may be another Ninth Doctor.