Pearl Jam: They are consistently creating music with integrity and soul. They don't advertise much, or create vido clips, because of how wary of the music buisness they are.
Radiohead. Another rock band that has integrity.
U2: They continue to innovate with new styles and at the same time have managed to not become gimmicky or bland.
Bob Dylan: Still rocking on, possibly he doesn't count cause he started in the 60's, but he continues to write new songs of merit.
FatboySlim: Some might disagree, but I think he is one of very few artists of his kind that is creating new music that is popular yet musically interesting. Time will tell whether he endures.
Red Hot Chili Peppers
Madonna
REM
Rage Against The Machine
Anyone else have some more? There are more bands that I like, but haven't listed, these are the bands that although I don't particularly like some of them (ie RATM), I think they are bands that go against the trend of one off hit bands.
"Dozens of people spontaneously combust each year, it's just not that widely reported".