I never experienced any true on-track feuds in my grand prix career, other than a couple of run-ins with Michael Schumacher. The difficulties there were a) he was very strong and successful in that period, and b) there was no talking to him!
When I suggested to him that he must've been wrong at least once in his life, he famously replied "not that I can remember". That's part of what made him successful, I guess.
Massa v Hamilton
DC says Hamilton and Massa are 'too nice' to become enemies © sutton-images.com
I think the on-going spat between Felipe Massa and Lewis Hamilton is a consequence of Lewis being off-form and finding himself on the back foot, and that's why he's found himself racing Massa instead of being right at the front. It's hardly Prost v Senna or Piquet v Mansell. They're too fundamentally nice for that sort of thing! There's no hatred between them as far as I know.