[lisper]

My favorite example, due to Douglas Hofstadter:

Politicians lie.

Cast iron sinks.

Politicians lie in cast iron sinks.

It's not actually ambiguous, but I think it's a lovely illustration of the subtleties of the problem.

An actually ambiguous example: I saw a politician lying in a cast iron sink.

[supernewton]

Ambiguous parses aren't even the worst of it -- the worst are the ones that require real world knowledge.

"I couldn't fit the trophy in my suitcase because it was too big."

"I couldn't fit the trophy in my suitcase because it was too small."

[thfuran]

Those seem like easier to resolve ambiguities than in the parent. One is almost certainly never going to be correct because it's nonsense, and that's a determination that requires a semantic understanding of the sentence, but no further context. The ambiguities in the parent are such that both parses are semantically reasonable. There are even contexts in which either could be intended. Suppose someone asks "What materials are heavier than water, and what are everyday things made of them that could float anyways?". If someone answers "cast iron sinks", it's unclear whether they're answering only the first, only the second, or even both, punningly.

[tmtvl]

My personal favourite example is the proof that two positives can make a negative: 'yeah, right'.