Here's a couple of work-arounds:
You could create a QuickLaunch toolbar within your Taskbar, and drag your shortcuts to that. Some or all of the shortcut icons could then be displayed on your Taskbar, depending on how much room (i.e. width) you allocated to the QuickLaunch taskbar area.
Add the Quick Launch Bar to the Taskbar in Windows
Quick Launch - Enable or Disable
Or, alternatively, you could create a Links Taskbar which is similar to the QuickLaunch taskbar.
Just right-click on the Taskbar, select "Toolbars" and then "Links." This will place a Links folder in the Notification Tray. Drag all your programs there and you'll have instant access to them without cluttering up your Taskbar. How to Use Toolbars in Windows 7 and Vista - Instruction Video (excellent and very clear)