http://www.ship3.fsnet.co.uk/warp_factors.htm (scroll down at the site for a chart)
Warp factor is the unit of measure for faster-than-light warp velocities generated by warp drive. Warp factor one is c, the speed of light, while higher speeds are computed geometrically under one of two different formulae. USS Voyager's warp capability is computed under the second formula.
The Constitution-class U.S.S. Enterprise NCC-1701 had a cruising speed of warp factor 6, and could reach warp 8 only with significant danger to the ship itself [TOS: Arena], but it nevertheless attained warp 11 in 2267 when modified by the Nomad device [TOS: The Changeling]. The Kelvans also modified the ship's engines to reach warp 11 [TOS: By Any Other Name]. The ship reached warp 14.1 in 2268 when the warp engines were sabotoged [TOS: That Which Survives].
It is not known whether warp 5 which could be attained by NX-01 Enterprise, captained by Jonathan Archer in the 2150s, was calculating warp factor speed by that or another method [Enterprise].
By the 24th century, a new warp factor scale was in use that employed an asymptotic curve, placing warp 10 as an infinite value.
Under the new scale, the Galaxy-class U.S.S. Enterprise NCC-1701-D had a normal cruising speed of warp 6 (392 times light speed, about warp 7.3 under the old system), and a maximum normal velocity of warp 9.2 (about 1649 times light speed, equivalent to about warp 11.8 in the 'old' system).
In 2370, following the formation of a massive subspace rift within the Hekaras Corridor, the Federation Council agreed that the use of warp fields posed a significant threat to some areas of space. Therefore the Council decreed that some areas would be limited to essential travel only. Furthermore, the Council imposed a Federation-wide 'speed limit' of warp 5, which could only be exceeded in times of extreme emergency [TNG: Force of Nature]. Later advances in Federation warp drive technology permitted the use of speeds exceeding warp 5. One of the first ships to be so equipped was the Intrepid-class U.S.S. Voyager, whose variable-geometry warp drive nacelles prevented damage to the subspace continuum.