Here's a way to do it without installing any software:
According to Gokul T.'s answer in answers.microsoft.com, while you can disable the thumbnail previews, you can't disable the hover list completely; however, you can apply a delay so that it doesn't show up unless you leave the cursor there for a while. Here are the instructions:
You can disable the taskbar thumbnail feature (sort of) in Windows 7 using a registry edit. This can be done by setting the taskbar thumbnail preview hover delay to a large value (say 10000 milliseconds or more), so that the preview is not immediately generated when you hover over a taskbar icon.
Click Start, type regedit.exe and press ENTER
Navigate to the following location:
HKEY_CURRENT_USER \ Software \ Microsoft \ Windows \ CurrentVersion \ Explorer \ Advanced
Create a new DWORD (32-bit) value named ExtendedUIHoverTime
Double-click ExtendedUIHoverTime and click Decimal
To increase the hover delay to 5 seconds, type 5000. Type 10000 for 10 seconds and so forth…
Exit the Registry Editor.
Restart your computer.
I tested this, and it seems to work.
Alternatively, if you don't feel like navigating around in the registry editor's interface, here's a script that should add the key with a delay of 10 seconds. Just copy the following to a text editor:
Windows Registry Editor Version 5.00
...and save it as a .reg file. You should then be able to double-click the file to automatically apply the changes in the registry. NOTE: I haven't tested this method, so I can't guarantee it works.