couple of obvious answers here from me
Barry Town, obviously, and lucky enough to support them through a few mad years when they had european football every year, which meant travelling around europe to watch your drinking buddies get tonked 8:0 by the likes of Dynamo Kiev. But it also meant great moment like seeing them play away in europe, seeing the likes of Shevchenko and Deco etc have to play footy at my local 2,000 seater ground and seeing a few euro wins, home and away, along the way. Seen them play literally hundreds of times.
St Pauli, just for the hell of it, a nice ethos and I do like a good loud choreographed sing song. Not been there, but I've been to The Zeitgeist in London on a matchday and that was fun. Bit of a hipster thing - I've even got the tee shirt! Went to a gig in Sankt Pauli shirt and the lead singer had the same shirt on! We bonded over a lager in the pub over the road just before the gig. Happy days. Never seen them live.
Valletta of Malta. I was working there when they won the league one year and managed to get on the team bus for the trip home through the street. Just mental, the palyers had a sound system on a low loader lorry singing quite a rude song about local opposition, Birkikara. Great memories. Seen them maybe 6 or 8 times.
But the only team that gets me pissed off for a Monday morning is Aston Villa. The only team where I try luck to influence a game (deliberately not watching, or deliberately wearing specific trainers on matchday etc.), is Aston Villa. I've stood on the original Holte End, I've seen 1970s violence outside, I've had corporate entertainment! I've sat next to Jimmy Rimmer! and I was there for the 5:1. I guess I've seen them around 70 / 80 or more times, probably more as there have been a couple of seasons a while back where I'd have saved money with a season ticket.