While train, bus and bike can get your quite far, in large enough cities it will still be a challenge to get to and from many places. Not in the city center, but in the outer areas where people commute to and from.
I live in Hamburg (Germany) where we have a subway, S-Bahn (similar) and a quite good bus network. Still, three big car sharing companies are successfully operating: Car2Go (by Daimler), DriveNow (by BMW) and Miles (private startup). They _do_ fill a need.
Another experiment will be started in April by the company I work for, MOIA (by VW): They provide ride sharing with a completely electric van (based on the VW Crafter) with 6 seats and permanently employed drivers. The focus is on the commuters who don't have a train-/subway-station nearby.
I think there are two lessons here: Just removing all cars will probably not work, we need at least intermediate solutions to slowly move people from owning a private car to shared solutions. And second, many of these mobility on demand/mobility as a service-solutions would be very hard to pull off without mobile phones and uniquitous mobile internet access.