From the Wikipedia:
"Bicycle sharing systems (also known as: community bicycle programs, yellow bicycle programs, white bicycle programs, public bikes, or free bikes) are increasingly popular and diverse. A number of bicycles is made available for shared use by individuals who do not own any of the bicycles. Public bicycles are a mobility service, mainly useful in urban environment for proximity travels. It enables to cut 3 breaks of a daily cycling use: home parking, theft and maintenance of your private bicycle." 
"Originally a concept from the revolutionary 1960s, bikesharing’s growth had been slow until the development of better methods of tracking the bikes with improved technology. This development gave birth to the rapid expansion of bikesharing programs throughout Europe and now most other continents.
There have been three generations of bikesharing systems over the past 40 years. The first generation of bikesharing programs began in 1964 in Amsterdam with the Witte Fietsen, or White Bikes. Ordinary bikes, painted white, were provided for public use. Individuals were to find a bike, ride it to their destination, and leave it for the next user. Things didn’t go as planned as bikes were thrown into the canals or appropriated for private use, so the program collapsed within days.
Nearly thirty years later in 1995, a second generation of bikesharing was launched in Copenhagen as Bycyklen, or City Bikes, with many improvements over the previous generation. These bikes were specially designed for intense utilitarian use with solid rubber tires and wheels with advertising plates; they could be picked up and returned at specific locations throughout the central city with a coin deposit. While more formalized than the previous generation, with stations and an organization to operate the program, these bikes still experienced theft due to the anonymity of the customer.
This gave rise to third generation bikesharing with improved customer tracking. In 1996, Portsmouth University in England launched Bikeabout using a magnetic stripe card which the student would swipe to rent a bike. The third generation systems inspired by the Bikeabout experiment were smartened with a variety of technological improvements, including electronically locking racks or bike locks, telecommunication systems, smartcards and fobs, mobile phone access, and on-board computers.
Bikesharing grew slowly in the following years, with one or two new programs launching annually, but it wasn’t until 2005 that third generation bikesharing took hold with the launch of Velo’v in Lyon, France. Today we’re approaching 100 programs globally with likely ten times this being planned as governments rush to implement bike transit.
To date, bikesharing programs have primarily been offered as a bonus to local governments by advertising companies, such as the big three of JCDecaux, Clear Channel, and Cemusa, who use their services. The local government gets a bikesharing program run by the advertising company and the advertising company gets locations for its ads and their revenues on public space. Such advertising includes billboards, kiosks, public restrooms, and bus shelters. It’s a convenient deal for governments who couldn’t afford to provide the bikesharing service otherwise.
As the demand for bikesharing increases, more companies have gotten into the industry and created their own technologies. Many of the new systems have no advertising component, but rather require direct subsidy from the local government in addition to user fees to be financially sustainable. These new bikesharing systems are allowing jurisdictions and universities either with populations too small to make advertising profitable or where advertising on public space is simply prohibited, to consider launching their own bikesharing services.
As we approach 200 bikesharing programs worldwide, the future of bikesharing is clear – there will be a lot more of it. Gilles Vesco, Vice President of Greater Lyon, France, attributed the following quote to the President of Greater Lyon, “There are two types of mayors: those who have bikesharing and those who want bikesharing.” This certainly seems to be the case as each bikesharing program creates more interest in this form of transit – call it a virtuous cycle.
My estimate of future growth of bikesharing is that it will become even more international as more cities around the world adopt it as their own. Europe certainly has the preponderance of programs due to forward-thinking elected officials and a greater commitment to cycling in general. The future will see even more growth throughout Western Europe, and moving into Eastern Europe, with cities of all sizes adopting their own bikesharing programs." 
"Bikes have several advantages as a mode of public transportation for short-distance urban trips because they:
- reach underserved destinations,
- require less infrastructure,
- are relatively inexpensive to purchase and maintain,
- generally do not add to vehicular congestion,
- do not create pollution in their operation, and
- provide the user with the added benefit of exercise.
In addition, bikes may increase trips on other modes of public transportation, as they expand the reach of trains and buses."