There was an "API Monitor" program, but it seems discontinued. Doesn't work on my system. Is there any such tool, which can work on Windows 7 x64? I need to log API calls from a selected set, better when parameter values.
http://www.bladeapimonitor.com/ seems to be doing what you need.
Depending on what you want to see, Procmon might also do the job.
Heres is an list of such tools: http://www.woodmann.com/collaborative/tools/index.php/Category:API_Monitoring_Tools. You could try the first one, its OpenSource and was last updated this year: http://jacquelin.potier.free.fr/winapioverride32/
Edit: You could try this one for x64 http://www.autodebug.com/
There's also Detours, free from Microsoft, it's a library to hook the windows API, but it's not a complete monitor program, you have to do some work to intercept the API calls.
With every version of Visual Studio comes Spy++ tool, which let's you monitor all messages in choosen process, window or thread, but not API, unfortunately.
API Monitor has been recently updated to include 64-bit support. The current version includes support to monitor over 10,000 API's and also supports monitoring of 600+ COM interfaces including Windows Shell, DirectX, DirectShow etc. Other features include call stack capture, monitoring of NT services, call tree display.
View a list of complete features, screenshots and downloads go to http://www.rohitab.com/apimonitor/