As a opinion of sound and music, I (myself with an opinion) believe they are the best band of all time, short lived or not. Heck punk bands most of the times didn't last as long as the Doors 3-4 year blast.
But take it in as this. In the late 60's, a time where there wasn't a real, true, American rock band, The Doors was there. They have to be the 60's best American rock band. You had Zeppelin, Who, Stones, etc who were all from the Europe invasion and you had the psychedelic rock from San Francisco and that was it.
But as a fan, I have 6 albums that I can keep listening to, as well as alot of live albums that continue to come out (with one just recently in November). So I am happy with the Doors being my fav.