Holmes would be difficult.
Can't imagine a relationship with Anna Kareina.
Alex [A Clockwork Orange] I'd move and leave no forwarding address.
Ignatius Reilly.
Uriah Heep.
Estella Havisham.
Shunkin [A Portrait of Shunkin].
Scarlet O'Hara.
Dorian Gray.

Just what comes to mind for books that I consider worth remembering.