Pink Floyd
Pink Floyd's The Wall and Dark Side of the Moon albums are regarded as some of rock's best. However, its their complexity that's also their undoing. Pink Floyd's albums always tell a story, but for some listeners that's just too much work.
Green Day
Though they're early punk rock legends, the poser-energy that Green Day gives off is palpable. They sing with fake British accents and pull melodies from other (better) bands. However, they've just been around so long and released their best album when it mattered most that loyal fans have stayed loyal.