I was a big The Doors fan back in the end of 90's when I was in college. I remember discovering that famous Oliver Stone's movie, then listening to all The Doors albums endlessly and maniacally for a couple of years.
Well, even though the band has never had an official bassist I'd say playing their songs on bass is fun! Mainly because the bass parts here are so much influenced by keyboards and are so melodic. Say the bass part of “People Are Strange” is very quirky and its melody doesn't repeat the main melody of the song which is always very cool for me. Try it!
Oh and even though I KNOW this part was meant to played with fingers I still played it with a pick just because I liked it better :) But you can go ahead and play it with fingers if you like.