Rotate view around vertical Y-axis What I want to do while modeling is start at the Top Ortho view (NumPad 7) with green Y-axis pointed up and down on the screen. I then want to rotate the view left or right around my model, moving only the X &amp; Z axis' while keeping the Y-axis vertical.  

Ctrl Shift MMB  zooms the view in and out if the wheel is held down and the mouse moved. If the wheel is scrolled the view rotates around the Z-axis.
Going to view 3 and Alt Shift MMB  allows rotating around a Horizontal Y-axis.

Is there a way to rotate around a vertical Y-axis?
By default, blender is set up with turntable navigation style, which means the Z is held vertical through your orbit manipulation. There is another style of navigation which used to be common in 3D, called trackball. This lets you orbit without the restriction of Z-up, but it also makes it easy to lose your sense of space in the scene. You can change this setting in the user preferences, under the input section. The left column contains those settings.

In 2.8+ &quot;trackball&quot; option is now in the &quot;navigation&quot; tab of the preferences: