[GOOD] Foursquare API gives public API rate limits.

[mmedjaoui]

The default limit is 500 requests per hour per set of endpoints per OAuth consumer per authenticated user. (If no user is provided, the limit is just per consumer.) This should be more than sufficient for any typical application. For example, if you write an iPhone application, every user who logs in with their foursquare account will be able to make up to 500 users/*requests and up to 500 venues/* requests, etc.
We allow 5,000 requests per hour to the venues related endpoints when making userless requests. For more details, see thevenues API. 

[mmedjaoui]

But this article of  https://foursquare.com/legal/api/platformpolicy needs to be considered carefully because in the same document you will find that

"Foursquare expressly reserves the right to limit the number and/or frequency of API requests in its sole discretion. If Foursquare reasonably believes that you have attempted to exceed or circumvent the rate limits (including, without limitation, through mass-registering of applications), your ability to use the API may be temporarily or permanently blocked, with or without notice, and without Foursquare liability to you or any other person."

I think it iw when you make more API calls than 500 requests per hour per authenticated user or 5000 for userless ones.