Like the rest of the bands listed by tuna, Harvey Danger was a one-hit wonder, but that hit rang out across the airwaves for months, years even. I know, I grew up listening to 105.9 (ALICE!) out of Denver in the late 90's and they played the same 25 or so songs over and over and over. Remember The Verve Pipe's "The Freshmen"? Remember Fastball's two hits? Remember Marcy Playground's "Sex and Candy"? What about the ever-ubiquitous Smash Mouth? Remember Joan Osborne's "One of Us"? Hey, Third Eye Blind got a lot of airtime as well. I remember all of these bands. Sometimes I wish I didn't. I have friends who still swear by Marcy Playground and Semisonic, but I never really cared for them.
I guess the one band of that ilk that's still kicking to some extent would be Nada Surf, who had a hit in the 90's and came back a few years ago as an indie act, and they got some fairly good press and are well liked, as far as I know.