Bicycles

Yes. A bicycle is a vehicle according to the UN’s 1968 Vienna Convention on Road Traffic. The UK is a signatory of this convention. The same convention considers that the person controlling a bicycle, whether riding or not, is an operator.
In the UK, in the late 19th century a pedal cycle was held to be a “carriage” for the purposes of the Highways Acts which set the basis for all road traffic law. So a cyclist had the rights and obligations of any other wheeled road vehicle – “a carriage of any type” of the time (including a prohibition from riding on the footway and an explicit right to use the carriageway). This remains in force. Pedal cycles are not covered by a great deal of legislation governing the use of motor vehicles, however (particularly the strict liability offences like speeding do not apply, as a pedal cycle does not have any requirement to have a speedometer; likewise the drink driving limits. In both these cases alternative offences for cyclists exist, but the definitions are subjective). In more generic language terms, a “vehicle” is any form of conveyance, or indeed any object or concept that literally or figuratively carries something else. So, yes, a bicycle is a vehicle for its rider.
There are over 2 billion bicycles in the world today.
The first bicycle ride was on a Laufmaschine at Mannheim on 12th June 1817. The rig became the “hobby horse” (after the children’s toy). In 1839 Kirkpatrick Macmillan balanced on two wheels mounted consecutively whilst in motion and developed the first mechanically propelled bicycle.  Early bicycles were limited by the shocking condition of roads. 
In the 1860’s Ernest Michaux and Pierre Lallement developed the first pedal driven bicycle whilst high-wheel bicycles (e.g. the ‘penny farthing’) were built for more speed. These early machines were considered dangerous toys. The 1880’s brought the ‘safety’ bicycle.  The first, the ‘Rover’ was built by John Kemp Starley in 1885. In the 1890’s John Boyd Dunlop invented the pneumatic tyre. The 20th century saw the introduction of the Roadster and ladies’ bicycles, which avoided skirts catching in the chain drive. Bicycle use declined in the US in the first half of the century; the opposite happened elsewhere. The Flying Pigeon brand in China sold 3 million units in 1986 and there was a waiting list for years. The last 50 years has seen an explosion in cycle popularity. There are now more cyclists in Britain than the Second World War. Most are cycling for pleasure. Advanced materials and computer aided design led to advances in design which has led to the enjoyment of cycling for sport and recreation. There are lightweight racing bikes, BMX bikes, mountain bikes, balloon tyre cruiser bikes, recumbent bikes, folding bikes, electric bikes and many other types.

In the less developed world the bicycle not only remains a vital and affordable means of transport for millions but also a means of carriage of goods for sale or to market for some of the poorest (see image).  The bicycle has also become articulated to provide a form of fee-paying passenger conveyance in many poorer countries.