There is no absolute limit per day or hour, however for the SOAP-API there is a recommendation to not use more than 2.000 SOAP-Calls per minute.
We recommend a limit of no more than 2k per minute for SOAP calls.
(Source: Intro to Marketing Cloud APIs)
As has been added in the comments, the Salesforce Support suggests not using more than 2,500 calls per minute when interacting with the REST-API.
Furthermore, there is a yearly limit associated with your Marketing Cloud Version/Contract:
Retrieve API Call Usage
However, there is currently no way of seeing the current usage in the Marketing Cloud Interface or via an API-Call itself: https://salesforce.stackexchange.com/a/272114/36218
Additionally requests are rate limited if your account's API usage is identified as having an impact on overall system performance (so also no hard limit there):
Marketing Cloud reserves the right to throttle SOAP API calls from a specific customer when those API calls cause slowed system performance. The throttling rate depends on the rate necessary to stabilize operations. If this throttling occurs, the business unit or user causing this issue receives HTTP 500 error messages communicating the limited rate until the calls causing the issue cease. Your Marketing Cloud account representative can help resolve the situation as necessary.
(Source: SOAP API Rate Limiting)
The REST-API at least has an error-type for too many requests:
Too many requests - Retry the API call after number of seconds specified in “Retry-After” header field. - HTTP 429
Too many requests - Your API requests are temporarily blocked due to too many concurrent requests. Contact Salesforce Marketing Cloud technical support to resolve the failure. - HTTP 429
(Source: Handle Errors in REST API)