Leeds is a common one - how I remember that goal they scored in the playoffs straight after the kick off from us scoring the goal that 'won' us the game. And the violence both real and perceived was certainly a big factor hence Leeds are also in my top 3 hated teams though they probably don't even think about us one bit.
Manchester City may seem strange to those that are very young or that are old enough to remember when they used to be a big club, but in the mid 80's City were shit and in a free fall to oblivion. They were a genuine rival to us and sometimes they were even our bitches. If you started your interest in football during the 80's you always had a feeling that we would beat City because we were often the better and IMO the bigger team.
Burnley is a strange one to choose Andy B - That Anglo Scottish final in the 70's when they thumped us left a scar on me that still itches today, but strangely they are a team I respect not hate. During the 80's they spent most of their time in the lowest division so I am not sure why you consider them rivals. So many of their players I had a soft spot for over the years. Leighton James, Peter Noble, Billy Hamilton, our own Stevie Taylor, David Eyres and Ron Futcher.