I got into the following bands way, way too late:
Led Zeppelin
The Beatles
Pink Floyd
Iron Maiden
Judas Priest
Rush
Fates Warning
My intro into music was essentially Survivor's Vital Signs, the Rocky V soundtrack, Bon Jovi, Whitesnake, and then finally Queensryche and Fifth Angel, where I noticed I liked more intense metal. For the longest time, while I dug stuff like Skid Row and Winger, and the whole late-80s pop metal movement (aside from QR, Fifth Angel and some others), it wasn't until the late-1990s I really expanded my knowledge. I became a fan of all the above bands, most recently, The Beatles' latter catalog. I became a big Maiden fan in 2000, for example. I became a big Rush fan about 2007 or so.
I guess with me, I get fixated on something, and just didn't give the classic bands a lot of attention. And then I remember one day I said to myself that I would go listen to all the bands that really influenced my favorite artist (the original lineup of Queensryche). I was going to give all of them the attention they deserved. And then boom, it all eventually clicked.
I'm now a hardcore fan of Fates Warning, Iron Maiden and Rush. I'd probably consider myself a solid fan of Led Zeppelin and a more casual fan of Judas Priest, The Beatles and Pink Floyd.