Every time you call a web method in the Partner API the response includes the Limit Info Header in the response.
<soapenv:Envelope xmlns:soapenv="http://schemas.xmlsoap.org/soap/envelope/" xmlns="urn:partner.soap.sforce.com" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<!-- ... -->
The header is also available in the REST API - Limit Info Header
With this you can monitor your API usage.
Merged from comment for completeness:
I'm interested in knowing how much API calls did my application consume. – Haris Osmanagić
This header is the global account across all applications. The documentation does mention a
API REQUESTS PER APP pilot that will provide limit quota information for a connected app. You could try and get on this pilot. Otherwise it is usually best if the application tracks its own usage.