The UCI has a set of strict guidelines as to what constitutes a bicycle for each cycling disciple (road cycling, mountain biking, etc.). These guidelines specifically state what they consider to be a bicycle, and are very important as any vehicle not adhering to them will not be able to race professionally.
The basic requirement is that the bicycle must be made out of three triangles - the chainstays, seatstays and seatpost form two (two chainstays and two seatstays, connecting to one seatpost) and the triange formed from the top tube, down tube and seatpost. This very neatly describes the vast majority of road bikes out there, while cutting out recumbants and highly specialised equipment (such as a specially moulded, super-aerodynamic time trial bike).
Of course, for some specialised events, such as downhill mountain biking and recumbant racing, the rules are relaxed a little, but you'll never see a recumbant in the Tour de France.
These guidelines serve to keep any one team from being able to out spend any other for an advantage, as well as keeping the sport 'pure'. They also often cited as an example that the UCI is staffed with luddites, especially in light of some carbon fibre frames that are now readily available, that have had weight added deliberately to keep them 'legal'.