My L2 saga:
I have one that I bought new in Feb. 1982 from Nadine's Music in Hollywood (ser. #173). It was my main axe until about 1989, and there were a couple of years in there where I actually said "I'll never play a bass made of wood again." (WRONG)

I did bring the L2 out on a gig a few months ago, and it sounded great. I also record with it once in a while - there are certain kinds of tracks where it still works better than anything else. There is an L2 in the design collection of the Museum of Modern Art in NYC, so I guess I own a piece of art as well as a unique, revolutionary instrument.
I would occasionally check out an XL2 or subsequent Steinberger versions if I ran across one in a store or elsewhere, and I never liked them as much as the L2. I prefer the neck profile on the the L2, and it just seemed more solid and substantial.
I had mine converted to fretless sometime in the late 80's and used it that way for a while, though I had frets put back in around 1990 (Rick Turner did both of those conversions). The L2 was killer as a fretless - totally even with no dead spots and great sustain. I eventually felt that a Jazz Bass-style fretless instrument was better suited for me, so I went back in that direction.
A few negatives about the L2:
The silk screened logo on the bass started flaking off almost immediately - Steinberger eventually went with a decal logo instead, which made a lot more sense.
The original frets were crap - I first needed a refret after about a year and a half. It's a difficult instrument to refret, as there is no truss rod, but fortunately I had some very good repair guys close by (John Carruthers, Rick Turner) who did a great job.
The screw on the swivel body plate always loosened by itself after a couple of hours of playing - I would always have to keep a coin handy to tighten it to the proper degree.
The Steinberger look does unfortunately have a '80's association that is hard to escape. It is my least favorite decade for music (even though there was obviously some great music made), and I have a particular aversion to '80's nostalgia, so.. that might have had an influence as far as retiring the L2.