I'm a big fan of shoegazer music. I was very much into it at one point, but maybe now a bit less...
Some of my favorites have already been mentionned by many of you...
My Bloody Valentine (Come in alone, When you sleep, Sometimes, Moon Song... )
The Jesus & Mary Chain (Just like Honey, Head On, April Skies, Darklands... )
Cocteau Twins (Amelie, This Love, Suggar Hiccup... )
The Clientele (Reflections After Jane, 2 am morningside, Monday's Rain, Porcelain, From a Window... I could really go on forever with this band

)
Slowdive I used to adore them and think their Souvlaki album was genius, but for some reason.. I am incapable of listening to them now..
It really is interesting to see bands with shoegaze influences.... I think some
Air and
Black Rebel Motorcycle Club songs have a bit of that...
and definitely a lot of earlier
Verve songs like She's a Superstar, Slide Away & maybe even Gravity Grave...