Although not a qualified pilot, I can claim that my favourite to fly is a Tiger Moth. As a youth I went up with a BA pilot who had one, and in between bouts of aerobatics that fully explored the flight envelope I had several goes. I enjoyed the feeling of it all immensely. I can see why so many other comments feature non-FBW aircraft.
Reading this thread and seeing the Chipmunk mentioned several times with fondness reminds me of seeing them buzzing round RAF Abingdon lots, decades ago when I was a kid. Happy memories. Thank you for the trip down memory lane :-)
Chipmunk, BAE-146, Tiger Moth mentioned by others: should I be surprised that DH-related aircraft feature lots?