Colorbox + jCarousel + slideshow + compact mode? I'm looking for a good solution (preferably as one integrated module) that would allow to display images in a multi-value image field in any kind of a lightbox, have a compact mode so that only the first image is shown, display a carousel beneath, and provide slideshow.

I've tried: Colorbox, Field Slideshow, jCarousel, Shadowbox. 

Colorbox was nicely integrated with Field Slideshow and provided a pager, but it had a strange bug which causes certain images on the main page beneath to be cloned upon every click within the Colorbox layer. Shadows wins over it even though is paid. Colorbox does not have a compact mode - if I set explicitly number of images to show to 1, all remaining images become unavailable and the slideshow is automatically disabled, otherwise, all of them appear on the node.

A while ago I gave also a try to Lightbox2, but I gave up on it, being unsuccessful at enabling its compact mode.
You basically want to output the images inside an HTML list, using, say views, and then install a jQuery plugin to do the slideshow for you.

You can use an existing module, however we often find it's easier to just install the jQuery plugin, and initialise your slideshow yourself.

Assuming your view outputs an HTML list, which is pretty easy to get set up, the rest isn't so much a Drupal question as it is a case of following the instructions for the exact slideshow plugin you're using.

We quite like http://jquery.malsup.com/cycle/ which has all the usual options, good documentation, and works well in a lot of different ways.