Building a Site-Specific Browser (SSB) is possible with technologies like Prism from Mozilla, but that doesn't do much for non-developer users. If all you want is an icon to click on your desktop to open a specific URL, and running the site in its own browser isn't what you had in mind, check out two apps: Fluid (download), for OSX, and Bubbles (download) for Windows. Both are free.
With Fluid, you can create as many SSBs as you want, control each of their preferences individually, and let them live where you need them: in the Dock, your desktop, or the Apple Menubar. I especially like the latter because I've created icons for four sites I check on and off during the day. Fluid, which requires Mac OS 10.5 (Leopard), also lets you create a single SSB with multiple panes fed from different sites, add a CoverFlow-like preview pane of links leading from the Web app you've desktopized, and will with a bit of Greasemonkey scripting it can alert you via Growl when something changes. Fluid is freeware, says it's creator, Todd Ditchendorf, and will remain so, although he's seeing over 20,000 downloads a month.
Bubbles for Windows lets you do much the same thing as Fluid. You can update your Windows environment with your latest Web apps as pop-up windows accessible from the system tray. Bubbles' developer, Ohad Eder Pressman, has gone to the trouble of prebuilding extensions for a dozen-plus popular Web apps: Want a Facebook bubble app that refreshes your FB News Feed every 5 minutes, or a Bubble that checks Gmail for you? You're done.
Users will always need free-form browsers for exploring the Web, but for their main Web apps, site-specific browsers can do a good job of imitating the local app experience.