I have to cheat and say I have two favorites!
In normal terms, I would say my 1965 Airline, because it feels like owning a bit of history to me (it's my only vintage). It might be a bit cliche because of The White Stripes, but Jack White was the first guitar player that really influenced me and gave me the bug, so it means something special to me even if it's a popular/celebritized model.
(Sorry I can't figure out why Lemmy is rotating it, it's not rotated on my phone)