My Recommendations:
Barenaked Ladies (not their popular stuff, except Pinch Me, Start with Gordon and move forward chronologically. You'll be pleasantly surprised.)
Ben Folds Five: All of it, excepting 'Fear of Pop,' which I'm not a huge fan of.
They Might be Giants are incredibly talented, start with "Flood" from 1990, go on to "Factory Showroom" and round it out with "John Henry", "Mink car", and "Apollo 18"
Postal Service & Death Cab for Cutie
Billy Joel, greatest hits volumes 1-3, and then sit down and listen to the entire 'River of Dreams' album
I mean, there's the obvious Beatles, The Who, Pink Floyd, then into the less meaningful but still awesome Styx, Boston, Supertramp, Kansas, Foreigner
I also happen to like Everclear, though their lyrics are a bit forced, and if you like alternative, Foo Fighters, Early Green Day, Nirvana (of course)
There's also 'ol Blue Eyes to consider along with Dean Martin and the rest of the Rat Pack; Etta James, Otis Redding, Marvin Gaye, Louis Armstrong, etc.
I mean, what are you in the mood for?