I won't sugarcoat it: for a kid growing up in the mid- to late-80's loving Sabbath, Kiss, Zeppelin, Purple, Priest, Scorpions, and basically anything that had the "NWOBHM" tag (Maiden, Leppard), The Cure were not my thing, to say the least. The closest I came was a closet admiration for REM.
Then I went and saw Page and Plant live in 1995, and Porl Thompson was the second guitar player, and two things happened: one, the band played an absolutely mesmerizing "The Song Remains The Same" (and I don't exagerate; after the song, I felt like I had blacked out and I looked at my friend and said "What the hell was that??" and he felt it too. We were literally transported by the music, I shit you not.), and two, P&P played this weird song I had never heard of (turned out it was "Lullaby").
I did a little investigation and found out who it was, and bought the album (Disintegration).
Then I got stuck (literally - I bought them for a friend and he bailed; well, his girl bailed and then so did he) with tickets to see The Cure in Hartford in the fall of '96 and figured, what the hell.
I was BLOWN AWAY. They were SO good live. Almost three hours, and although I only recognized about three songs, it was captivating. Robert Smith wore a Hartford Whalers jersey all show and while that is usually a lame cliché, it was cool and they played so well. With the music and the lights and the atmosphere... even though I don't care for some of their earlier stuff, and I'm only familiar with maybe 20 or 25% of their catalogue, I do consider myself a big fan.