I use Boston's bikeshare (Hubway) all the time, even though I own one bike and could easily buy another.
Advantages:
One-way trips. Bike from one Hubway station to another, then go home on the bus or train or in your friend's car without needing to figure out what to do with your bike. I do lots of circular itineraries where I switch from bus to bike to strolling to train to bike and back to bus without ever retracing my steps.
100% secure bike parking at any Hubway-equipped destination. Because bikes stolen from Hubway stations are not my problem, they are Hubway's problem, so once I dock a bike at a station I just walk away with no worries.
(And right there we've probably got my $85/year of value. Imagine a service which provided lighted, security-monitored bike racks at forty or fifty stations around town, with insurance against theft and an iPhone app to tell me if a particular rack has space for my bike at this moment. I might well expect to pay $10 a month for that service. And Hubway provides that, plus they throw in bikes for free!)
Minor advantages include spontaneous bike trips (mitigated by my own insistence on wearing a helmet, which is annoying to carry around "just in case") and much faster arrival and departure because unlocking and locking these things is fast. I walk up and leave in thirty seconds, most of which is spent putting on the helmet, readjusting the seat height, and strapping my bag to the bike basket; arrival is faster, maybe fifteen seconds. Looking for a good locking spot, then fiddling with U-locks is not so much fun as that.
Meanwhile, sure, thieves could strip the bikes at a Hubway station. I'll bet they'd be doing it on camera the whole time, though, and Hubway stations tend to be near major intersections in populated neighborhoods. And Hubway bikes are pretty odd; I'm not sure there's a lot of easily-fenced standard parts on there.