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You can change the time display in the taskbar to also show date. Or, remove it all and show nothing there. Here's how:

(Requires a registry edit)

To show nothing:
HKLM\Software\Microsoft\Shell\TBOpt = 0 (DWORD decimal)

To show just the clock:
HKLM\Software\Microsoft\Shell\TBOpt = 1 (DWORD decimal)

To show just the date:
HKLM\Software\Microsoft\Shell\TBOpt = 2 (DWORD decimal)

To show both the date and the clock:
HKLM\Software\Microsoft\Shell\TBOpt = 3 (DWORD decimal)

Important Notes!
1. If you switch to the view the Analog clock the date will remain visible.

2: Even if you remove the clock, the space there is still reserved and will block any icons that are shifted over to the right.

3: The date may be blocked by the space reserved for the OK/Close button in the top right hand corner of the screen. You can fix this by adding spaces at the end of your "Short Date Format".

Restart. You may have to play around with this one a bit more...