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Historical examples:
Croesus asked the oracle what would happen if he attacked Persia. The reply: ‘A mighty empire will be humbled’.
Thank you so much for the book. I shall lose no time in reading it.
Modern example:
I am opposed to taxes which slow economic growth.
Humorous:
The anthropologists went to a remote area and took photographs of some native women, but they weren't developed.
What is the term used for these examples?
These are examples of amphibology. To quote its Wikipedia entry:
Amphibology or amphiboly (from the Greek ἀμφιβολία, amphibolia) is an ambiguous grammatical structure in a sentence.
These are examples of syntactic ambiguity. They demonstrate ambiguity between alternate syntactic structures underlying a sentence.
See http://en.wikipedia.org/wiki/List_of_linguistic_example_sentences for this and other types of lexical ambiguity.
The sentence in your title contains a classical figure of speech commonly called zeugma (your other sentences are rather double entendre or simply ambiguous, as the others have mentioned). See Wikipedia on zeugma and syllepsis; what Wikipedia calls syllepsis is usually simply called zeugma, as syllepsis is the most common significant application of zeugma in rhetoric and literature.
Zeugma (from the Greek: ζεῦγμα, zeûgma, meaning "yoke") is a figure of speech describing the joining of two or more parts of a sentence with a single common verb or noun. A zeugma employs both ellipsis, the omission of words which are easily understood, and parallelism, the balance of several words or phrases. The result is a series of similar phrases joined or yoked together by a common and implied noun or verb.
...
Syllepsis, also known as semantic zeugma, is a particular type of zeugma in which the clauses disagree in either meaning or grammar. The governing word may change meaning with respect to the other words it modifies. This creates a semantic incongruity that is often humorous. Alternatively, a syllepsis may contain a governing word or phrase that does not agree grammatically with one or more of its distributed terms. This is an intentional construction in which rules of grammar are bent for stylistic effect.
See my answer to a similar question here: Books and other things with the same name .
Those are examples of double entendres.
While previous answers have correctly described the technical names for the ambiguity contained in these statements, I believe that they represent an inherent ambiguity and lack of structure in modern English that is less present in other languages.
For example, my son eats "Organic Baby Rice". Is this rice made of organic babies? Similarly how is a "bamboo cage" different to a "bird cage"? One implies a cage constructed of it's modifier, another the intended prisoner. For comparison, French distinguishes between "riz de bébé" and "riz pour bébé". While these examples are trivial, I believe they illustrate the point.
This is an example of a Garden Path sentence
Could this be a "dangling participle?" The famous one in medicine is "Studies on monkeys using endoscopes," but then someone remarked that there is always a monkey at the end of an endoscope.
Those are examples of dangling modifiers. A dangling modifier causes ambiguity in a sentence because the object to which a modifier refers is unclear.
