To be classified as a Wheat Beer a large proportion of wheat is used in addition to, or instead of, malted barley. If the wheat is added merely as a supplement, such as for head retention then these would be considered as variant on whatever the base beer is. Due to the use of a high proportion of wheat the overriding characteristic is that they will usually be cloudy in appearance, though they don't necessarily have to be.
The most famous Wheat Beers come from continental Europe particularly Germany and to a lesser extent Belgium and the Netherlands. In Germany Wheat Beer is often called Weißbier / Weissbier (white beer), Hefeweizen or for darker versions Dunkel Weissbier. In Belgium Witbier is often used and their beers are often subtly flavoured with coriander seed or orange peel.
Colour
Yellow to gold, but 'Dunkels' can be brown
Clarity
Hazy to cloudy, but clear examples exist
Carbonation
Low for cask, but bottles and cans are heavily carbonated
Alcohol
Not detectable
Hop
Evident throughout but balanced by the malt
Malt
Strong malt presence but softened by the high proportion of wheat
Esters
Fruity notes are common, banana being the most prevelant
Phenols
Spicy note such as cloves can often be detected
Fermentation By-Products
Distinctive cloudy in appearance due to the amount of wheat used
Body
Medium to full
Carbonation
Low but can be higher in bottled and canned examples
Finish Length
Medium
Attenuation
Soft and sweet
Hops
Generally a small amount of noble hops are used such as Hallertauer, Saaz, and Tettnanger.
Malt
A significant part of the malt bill is Wheat rather than Barley
Water
No specific requirements
Yeast
Traditionalists would rely on a 'Munich' style yeast
Black Hole - Milky Way