What does web service error 606 mean?

Where are you seeing this error? If it is related to the REST API, then it is a rate limit error. 

Yes, Thank you.

I have also seen a 607 error and a 601 error at different times as Web Service Errors.  Could you tell me what those mean, as well?

607 means daily REST API quota was reached. 601 means the access token used to make a request to the REST API is invalid. 

The full list of error codes is documented here:
http://developers.marketo.com/documentation/rest/error-codes/

Thanks!  I totally forgot about the dev site! :)