Bear left at zoo. (Do you turn left when you get to the zoo, or did someone leave a bear there?)
I'm going to sleep. ("Going" can be a verb with destination "sleep" or an auxiliary indicating near future. There is little difference in meaning between the two parses.)
The word of the Lord came to Zechariah, son of Berekiah, son of Iddo, the prophet. (Which of the three is the prophet?)
British Left Waffles on Falklands (Did the British leave waffles, or did the British left waffle?)
The cow was found by a stream by a farmer. (The farmer found the cow; she was located by a stream.)
For philosophical considerations of ambiguity, see ambiguity.