I know of at least two AIs in "classic" literature that have not been mentioned yet. Both are examples of "emergent" intelligence - where the AIs aren't just turned on from being built and think right away, but gradually become aware of themselves:
Sven from
The Turing Option by Marvin Minsky and Harry Harrison.
(That one is perhaps my favourite example of this particular sub-genre.)
H.A.R.L.I.E from
When H.A.R.L.I.E. Was One by David Gerrold.
BTW: This is one of my favourite subjects. I have a Philosophy degree, and questions of mind, perception, and identity were my main focus.
Later: Oops! theducks did mention When H.A.R.L.I.E. Was One.