Is it possible to script that during installation to download files from a web server with Inno Setup?
InnoTools Downloader, recommended by the accepted answer, has not been updated since 2008. It does not work with Unicode version of Inno Setup (so it does not work with Unicode-only Inno Setup 6) and does not support HTTPS (among other). Do not use it.
I'm re-posting the answer by @Jens A. Koch, which has been deleted by moderator for some reason:
You might use the Inno Download Plugin by Mitrich Software.
There's also DwinsHs (Downloader for Inno Setup). And Inno Setup 6.1 will support downloads nativelly.
Take a look at the InnoTools Downloader (http://www.sherlocksoftware.org/page.php?id=50).