Shooting reflections is favoured not only by amateur photographers but also by professional shooters. More often than not reflections add interest to the picture which also show the photographer tries to be different in composing his/her photograph. At times it conveys a message or tells a story just by using reflection.
The way reflections result totally depends on the type of surface the image falls on. Just like how an image is produced by a filter. While a mirror would normally produce a reflections just exactly like the original image the water surface or glass would alter the colour, shapes, appearance and even size of the original image and produce interesting reflections. Reflections can be captured together with its source image or more interestingly it can stand alone as a subject especially when the reflection has gone beyond recognition and becomes abstract-like and impressionistic pattern. The possibility is endless, the only limit is the photographer’s creativity.
Behind the Gare St. Lazare by Henri Cartier-Bresson wouldn’t have been so special without the reflection of the jumping man. Without the reflection we wouldn’t know that his heel did not touch the water surface yet at the “decisive moment” Henri Cartier-Bresson clicked the shutter. And in case you are not aware Henri Cartier-Bresson didn’t shoot using a camera with 8fps shutter speed but it was a 35mm Leica manual camera fitted mostly with only 50mm lens. Such is the classic example of the decisive moment as claimed to have been coined by Henri Cartier-Bresson himself although at a later part of his life he admitted he never coined such phrase.
Fully symmetrical image horizontally is always preferred for landscape and it always proves to be a successful formula. This method is frequently adopted by one of my favourite landscape photographers, David Noton, whose reflection shots in his landscape works are nothing but breathtaking. Meanwhile Andy Long has some enlightening tips on shooting reflection here. And Russ Burden shares some good tips on shooting reflections in nature photography here.
There is also an article by John Harvey concerning reflections which is considered as part of compositional aid.
If you feel like browsing some sample reflection shots, don’t hesitate to view the past Apogee Photo Contest with the theme Reflections.
I admit I am also fond of shooting reflections no matter it is architecture, landscape or portraiture. Almost always there are reflections anywhere you shoot, so use it to your advantage and no harms experimenting. Here are some of my favourite reflections shots:

A horizontal shot with symmetrical composition, half containing reflection.

Here the prime subject is the reflection itself which looks like an impressionistic painting.

Reflection of my wife in the mirror captured while she was busy shopping for headscarves.

Intan on her wedding day.

A little different kind of reflection of the Malaysian flag resulting from diffractions of light by water drops.

A bride mannequin and the reflection of old shophouses.

A Malay bride, Nana, in the mirror just after being made up.

The Asy-Syakirin Mosque in KLCC area and its little reflection from the nearby pool.