If you want to download games go here. Those are the free ones that AG allows you to download. If you're talking about something else, I cannot help you.
I know a few ways of downloading flash games. Both through an application, directly from the page and on websites. Though you should be careful about this. If you want to download games that are not offered on the developer/publisher's site without obligation or anything, you will have to ask the permission of the developers and publishers.
Guess that only counts for people that either have no continuing internet connection or have a slow connection, then I can fully understand! Otherwise I'd say... play them online, saves you the harddisk space!
Well, apparently playing them games downloads the .swf file every single time you play, which consumes bandwidth. Downloading it to the hard disk eliminates that waste of bandwidth.