I see several votes for the Toadies here...they no longer exist.
Same for Soul Coughing, a band I sadly lament and had the chance to see many times. Fantastic. Although M Doughty (frontman) is releasing a new solo lp this week called Haughty Melodic. I've seen him do all these tracks live acoustic many many times, and you just can't describe his unique brand of shuffling white boy folk rock beat poetry "small rock" .
I also see Slowdive mentioned - another defunct band...try some My Bloody Valentine on for size. Or maybe check out Adorable's Against Perfection - a fantastic creation era shoegaze band that was terribly overlooked. Rachel Goswel and Neil Halstead went on to form Mojave 3. Another fantastic band that is very much so less shoegazey and very much more Nick Drake / Gram Parsons.
A few others I agree with or would like to add to the list...
M83 - Explosions in the Sky with bit-tones is a pretty good description
Black Moth Super Rainbow - indescribable loopy weirdness based around vintage synth and moog tones. think early 70's sci fi shoved into the next millenium...
The Appleseed Cast - My current fave and I champion these guys every chance I get. The early catalog is shades of Sunny Day Real Estate...but somewhere along their career, something wonderful happened and they became this fantastic ambient trippy dreamy guitar band. Waves of washed out delay bring to mind thoughts of shoegaze, but the intertwining melodies shove this out ahead of the pack. Mid career they released a 2 cd set of a single body of work. Low Level Owl Vol. 1 and Vol 2. You can buy these seperately, but I highly recommend purchasing both and listening to it as a whole. Beautiful and shimmering guitar based ambience.
I could write about this all day, but my boss would probably kick my ass. More later.