When you're opening page in IE it downloads lots of files, including CSS, scripts, pictures, SWFs, etc. I need to develop small plugin which will monitor all these URLs and let's say save to file this list.
I need it in Delphi, but any example in any other programming languages will be really appreciated.
You need to make a Browser Helper Object (BHO). I'll re-tag the question for you. Here's a SO search for questions tagged BHO:
http://stackoverflow.com/questions/tagged/bho
Even a BHO won't really work very well for this. Technically, you could write a BHO that wraps the HTTP and HTTPS protocols using an APP-wrapper, but this is unsupported, causes performance and crashing problems, and is very hard.
If you're using .NET, you can pretty easily host FiddlerCore (www.fiddler2.com/fiddler/core/) and you could probably wrap it with Delphi, but this is meant more for testing than production use.