A canonical example of syntactic ambiguity in the english language. There are two (or more?) readings of this sentence, and two logical responses:
1) Why can't I? Are they camera shy?
2) Of course. Wooden objects generally make very poor imaging devices.
A linguist will tell you that the sentence has two valid parse trees. The first interpretation has "with a wooden leg" on the same level as "a man", while the second has it modifying "take a picture".
An AI researcher, or one who has done work on natural language recognition, will tell you this is the fundamental difficulty making computers understand natural languages. Both interpretations of the sentence are syntactically valid, and both interpretations are well within any reasonable threshold of sensibility. On one hand, "a man with a wooden leg" is a fairly common form for the term "wooden leg" to exist in, and the concept of taking a picture with a wooden leg is pretty ridiculous. On the other hand, a logical agent with the ability to sense the intentions of others (second order reasoning) would have a difficult time understanding why anyone would want to tell them that the photography of amputees was prohibited.
Other examples used to express this concept are "He saw the girl with the binoculars," and "Make me a sandwich." See also time flies like an arrow.
says: And a sentence that thankfully would not exist in Chinese
...one reason it is so easy.
says: There's still a third reading, i.e. you can't physically grab any of these pictures of men with wooden legs. They belong to someone else...
(This is an example of semantic ambiguity, not syntactic. The confusion occurs not because of multiple parse trees, but because the word "take" has two meanings. The parse tree is the same as that of meaning 1 above. By the same token, meaning 2 could be changed to mean "You can't take a picture of a man with a wooden leg because wooden legs don't have opposable thumbs." See I am forced to smoke my cat for more semantic ambiguity. -ed)
says: though this is silly and nitpicky: it would also be quite valid to interpret the sentence as "if you have a wooden leg, you cannot take a picture of a man"