Pink Floyd is the band that comes to mind based on what you said you're looking for, if for some reason you already haven't heard their stuff. Check out the albums Dark Side of the Moon and Wish You Were Here to start off. If you have a decent sound system with a DVD player, buy their live concert dvd PULSE.
If you're looking for newer stuff, check out Porcupine Tree and Blackfield. Steven Wilson is the lead singer and guitarist in both these banRAB and he is pretty much the modern day Gilmour.
I actually haven't heard the first Blackfield album yet, but I have heard Blackfield II and it is pretty sweet. Very mellow and a little more pop oriented than porcupine tree.
Start with these albums for Porcupine tree:
In Absentia if you like harder rock
Lightbulb Sun if you like softer rock
Deadwing for a mix between the two
It's hard to describe Porcupine Tree as any genre, but if I had to I would say it is Progressive Rock. There are many themes to their music, much like floyd.
If you have a decent sound system with a DVD-A player, I highly recommend getting the DVD-A versions of the albums, the quality is reference on all of them.
