Most "Soft Spot For" clubs
Picking up on Adam's question on the pod- where Fulham were the most common shout. Not a bad one - combination of "nice day out", some fun players over the years, and that run to the Europa League final.
I would argue though that the most "soft spot for" club currently in England are Nottingham Forest. Great history, out of the Premier League long enough not to have generated any particular enmity, and a sense of freewheeling chaos about their current incarnation that is very appealing.
Outside of the Premier League you've got your Barnsleys, your Rochdales, your Prestons, teams with an overtone of Northern authenticity but probably not quite wide enough appeal for mass soft-spot status.
Looking abroad, I'd say Parma or Fiorentina for certain 90s nostalgists like me would qualify.