They might not be the best band ever or even in your favourties now, but you loved them first...who fits that description for you?
For me its Apache Indian; a rap artist, with mostly repetitive but unique sound(and did some work with Maxi Priest). I don't particularly like him now, but I'd bought all his LPs at a time. He had one huge hit(Boom Shakala) which even now sounds damn good to me, but thats all.

Oh, and I'm posting this here so that genre barriers are not considered

I have to say I got really into the Beatles well before I got right into any other band or artist. My brother put me onto them... he'd seen the Beatles Anthology on TV, and then decided to buy every single Beatles album available on tape at the time.
I think we have all but one album by them, now. Anyway, I got right into the Beatles, even going so far as to put a picture of them on my 4th grade English book. Crazy, huh??

Well yeah, that was the first time I feel in love with a band, I think!! (Their music, that is!!)

That would be Rush. I was on a school trip to Germany and my room mate had a crappy cassette player with him. He listened to Exit Stage Left all the time, but it was the start of side 3 (of the double 12" album), Broon's Bane and then The Trees that got me. I've had a weakness for finger-picked acoustic guitar introductions ever since. I went out and bought pretty much everything of theirs that I could afford and didn't listen to much else for a few years.

I'm trying to work out how I moved on from there, but it's hard to remember the order in which I bought things. Pink Floyd and Led Zeppelin I think would be the next two milestones, and Jethro Tull. What I do know is that I am rediscovering things now that I thought were rubbish at the time, which could turn out to get a little expensive as I fill all the gaps in my collection.

the red hot chili peppers

Led Zeppelin for me... It was Kashmir that did it.

Probably Green Day.

Pearl Jam and Nirvana for me.

The first ever was Blur.

The Beach Boys or Steve Miller

Green Day was the first band that I really liked.