Car sharing and ride sharing are two very different things, as has been pointed out. Car sharing is essentially rental by the hour, and requires you to drive the car yourself. Services like Uber, Lyft, and Sidecar are ride sharing, and they did start out as true sharing of a trip the driver was already making, although they seem to have morphed into taxi services with drivers cruising around picking up fares.
I've used car sharing numerous times and am a big fan of it. I drive rarely enough that there is no way owning a car would be worthwhile, but it's a nice luxury to have access to one when it's needed. I'd like to see car sharing supplant private ownership of cars as the norm. (I wish it existed where I live now; I haven't driven in 5 years because it doesn't.)
I've used ride sharing (Sidecar) only once, when my boyfriend and I visited a museum and he was too unmotivated to walk the 1.5 miles back to the train station in the heat. I felt rather decadent! But the car was in much better condition than any taxi I've ever ridden in, and the driver was very good. Taxi drivers, on the other hand, really scare me.