I've never followed another club, but I have been to see Bury a couple of times as a teenager many, many moons ago as well as Altrincham, Stockport and oddly enough, Chelsea!
*Edit*
Also did a work colleague a favour and took her husband to see Liverpool v Strasbourg at Anfield years ago too.
*Edit2*
Forgot to add spent a weekend in Ayr and as they were playing at home, went to watch them too.