Obtaining more than 20 results with Google Places API

Now it is possible to have more than 20 results (but up to 60), a parameter page_token was added to the API.

Returns the next 20 results from a previously run search. Setting a page_token parameter will execute a search with the same parameters used previously — all parameters other than page_token will be ignored.

Also you can refer to the accessing additional results section to see an example on how to do the pagination.

UPDATE: Since I originally wrote this answer, the API was enhanced, making this answer out of date (or, at least, incomplete). See How to get 20+ result from Google Places API? for more information.

ORIGINAL ANSWER:

The documentation says that the Places API returns up to 20 results. It does not indicate that there is any way to change that limit. So, the short answer seems to be: You can't.

Of course, you might be able to sort of fake it by doing queries for several locations, and then merging/de-duplicating the results. It's kind of a cheap hack, though, and might not work very well. And I'd check first to make sure it doesn't violate the terms of service.