Let's say I have address as text:
901 Cherry Ave. San Bruno, CA 94066 USA
is there any FREE service, which can help me to identify GPS coordinates (longitude and latitude) of this address? (I'll use that in my application, so it should be some kind of API)
The text can be in any language.
The process is called of converting address to geographic coordinates is called geocoding.
Depending on how you'll be using the data, there's an API available from Google, details here. Good luck!