Also worth pointing out that in languages which do divide the words, they often divide the words too much, such that the individual words have little to no relation to the meaning of the longer phrase. E.g. new york, arm and a leg, kick the bucket.
This, over-dividing problem, along with the under-dividing problem you mentioned, are both huge hurdles for machine textual understanding and machine translation systems.
On the information-extraction system I'm working on now, roughly 80% of the entities we're trying to extract are multi-word expressions. Very difficult.
[1] https://en.wikipedia.org/wiki/Multiword_expression
[2] http://aclweb.org/aclwiki/index.php?title=Multiword_Expressi...