Taking website screenshot, server-side, on a Linux rented server, free

PhantomJs is the solution

if(phantom.state.length === 0){
  phantom.state = '0_home';
  phantom.open('http://www.mini.de');
}
else if(phantom.state === '0_home'){
  phantom.viewportSize = {width: 800, height: 600};
  phantom.sleep(2000);
  phantom.render('home.png');
  phantom.exit(0);
}

http://cutycapt.sourceforge.net/

CutyCapt is a small cross-platform command-line utility to capture WebKit's rendering of a web page into a variety of vector and bitmap formats, including SVG, PDF, PS, PNG, JPEG, TIFF, GIF, and BMP.

There is no PHP-api, but you can always use it through PHP's exec functions.

Here is a better script using phantomJS 1.5

var page = require('webpage').create();

page.open('http://www.google.com', function() {

    page.viewportSize = {width: 1024, height: 768};
    page.render('screenshot.png');
    phantom.exit();
});