Cryptsy, Mintpal and Bittrex have public APIs.
How many requests per second or minute can I do to these APIs?
Mintpal has a limit of 10 requests/second
MintPal API v1 offers a simple REST API to retrieve information about our markets. The API responses are JSON encoded arrays. Please be aware that calls to the API are rate limited to 10 requests per second, any requests exceeding this rate will be met with a HTTP 503 response.
I know Kraken has different rules. You can 'burst', instead of a flat limit. Source
The basic API rate limit is 1 call every 5 seconds. You can do faster bursts up to 10 calls, but then you'd need to follow that by a 50 second pause before you could resume the 1 call very 5 second rate. If you get locked out, it's for 15 minutes.
For really active traders (including those who want to market make with us), we can offer much higher limits. Anyone interested in this should contact us with a support ticket.
I know Kraken isn't on your wishlist of things to know, but I cannot find information about Cryptsy or Bittrex. But it gives you a insight at real limits, so you can maybe assume those two have similar limits.
For Bittrex, this post mentions they got banned for a week for spamming the API. The email they received from Bittrex lifting the ban said to limit to 1 request per second.
Unfortunately, there is still nothing on their official documentation, and I've found their support to be slow-never to respond.
So we're stuck with hearsay for now.