The historic view: lifts and inclined planes were uncommon, and there is little trace left of most that were built. They were used for climbs which would have required a flights of numerous, closely spaced locks. Such flights were considered bottlenecks in the canal system and it was concluded that canal traffic would move much more quickly through a single lift or inclined plane, and save water in the bargain. However, these were mechanical contrivances and maintenance difficulties caused many to be replaced by the flight of locks that they had been designed to avoid.
In recent times, lifts and inclined planes have been put to good use on continental European waterways. See examples, labelled modern, below.
For a book on this subject, see Canal Lifts and Inclines of the World, by Hans-Hoachim Uhlemann.
The photo, by Rob Barker, shows the Anderton Lift as it looked in 1982, prior to its closure, when the lift was still electrically operated.
Additional photos from 1980 by Philip and Pete Payzant
The Original Henrichenburg lift-lock - in Germany; operated 1899-1962 (web page in deutsch, english, francais, nederlands) [Thanks to Eckhard Schinkel for directing me to this one.]
"submarine lock" - boats travel up and down underwater in a closed caisson. Operated on Somerset Coal Canal for two years in late 1790's. Further details will be found at this Somerset Coal Canal (Society) web page, under "caisson lock".
The web page entitled "Variations on tank-based lifts", formerly linked to here, is no longer available but the balance lock wikipedia page may provide similar information.
Modern examples: Wikipedia has a List of Boat Lifts, with links to individual lifts. A good example of a conventional modern lift is the Strépy-Thieu boat lift in Belgium. For a unique modern design, see also the official Falkirk Wheel page or Falkirk Wheel. The Wheel reconnects the Forth & Clyde and Union Canals between Glasgow and Edinburgh.
See also Terry Fogarty's concept for a Diagonal Lock.
Comprehensive book on boat lifts (in German):
Eckhard Schinkel: Schiffslift. Die Schiffs-Hebewerke der Welt. Menschen - Technik - Geschichte. Essen, Klartext-Verlag 2001. ISBN 3-88474-834-3
Another modern example is the inclined plane of Ronquières, in Belgium. It has a higher lift than St Louis-Arzviller, but is much less steep. (Aussi, en francais, le plan incliné de Ronquières) [Thanks to Kenny Staelens for suggesting that the Ronquières plane should be mentioned here.]
Here's an old picture of the Foxton Inclined Plane in operation (37K), year unknown, obtained by Rob Barker from an otherwise unlabelled postcard. Further details, and restoration plans, may be found at the web site of the Foxton Inclined Plane Trust.
A surviving, but not working, example of an historic plane can be seen at the Blists Hill site of the Ironbridge Gorge Museum. This is the Hay Incline of the old Shropshire (tub-boat) Canal. The vertical drop is 207 feet. An article mentioning this plane, and other inclined planes that existed in Shropshire, appeared in the Oct 2003 issue of Waterways World.
Though most planes move a boat while suspended in a tank of water, some carry a boat out of water in a cradle. There are five planes of this type on the Ostroda-Elblag Canal in Poland. (See the article in Oct 2003 Waterways World.) Another is in Canada, on the Trent-Severn Waterway, and is referred to as the Big Chute Marine Railway.