Helping people with computers... one answer at a time.
The task bar is a busy place, and there are lots of things on it; the start button and menu, the quick launch bar (if you have that enabled) and on the far right, the notification area. Most all of those are configurable to some degree, but the area where buttons representing your "currently running programs" is not. It's always supposed to be there, there's no way to turn it off.
As a result, no way to turn it on should it disappear.
Well, no obvious way.
Unfortunately, I have gotten reports of the "running programs" area going away. I have no real idea of how it happens, but, clearly, it does.
Restoring, while not obvious, is not hard. It appears to only need a registry change and a restart of Windows Explorer.
Kelly Theriot, a Microsoft MVP, has a set of tweaks available at Kelly's Korner. They're fairly light on documentation, and perhaps even a bit techie if you want to understand them. On the tweaks page scroll down to item #240, and click on "Programs Aren't Minimized in the Taskbar". That will run, or download, a "vbs" (VBScript) program which will, after confirming, reset the Taskbar's properties. Note that several other aspects of the Taskbar will also be reset to their default states, but you should get your "running programs" area back.