Is there a keyboard shortcut for the method dropdown list in Visual Studio 2010's VB.NET code editor?

Ctrl + F2 is assigned as a default shortcut key to move the cursor to Navigation Bar. (L.H.S is classes dropdown and R.H.S is methods dropdown.)

You can use Tab to jump to methods dropdown.

The whole combination that you need is Ctrl + F2 + Tab.

Hope this will help you.

CTRL+ F2 and Tab can access that dropdown list. I was not able to find the direct short-cut for that dropdown list for long time.

Tools->Options->Environments->Keyboard can assign some short-cuts manually.