I created a box as a first object in a new scene. I then angled it 45 degrees on the x axis. This is my starting position. I hit Set Key and placed a key at frame 1. I then moved the time slider to frame 100, rotated the box along its local z axis 180 degs and placed a ket at that frame. When I run the animation, the box spins around the world z axis. How can I make it spin around the local box z axis?

Create the Box. As the Pivot will be on the main XY plane, you might want to move it to the centre of the box (Hierarchy Panel > Affect Pivot Only > Center to Object).
Animate the rotation with the box in its original orientation.
Create a Dummy, align it to the box. Select and Link from the Box to the Dummy. Rotate the Dummy to the desired angle. The Box will continue to rotate as you intended.

Max 4.2 through 2013.
XP-64 (SP2)
NVidia 9800GTX-512 (Driver 266.58).
Core 2 Quad Q6600 2.4GHz, 8Gb Ram, DX9.0c.

...and thirdly, rotations in 3D are actually a very problematic sort of math. Paul Neale has an excellent page explaining this: http://paulneale.com/tutorials/rotations.htm, rotation is near the bottom of the page. Short story: it’s not a bug, it’s not peculiar to Max; it’s the nature of the wacky math involved. You can learn still more if you search “gimbal lock” and 3D rotation.

-Jeff

Max/Composite 2012 (subscription)
Win7-64pro, Intel i7-hex on SuperMicro mobo, 12 GB RAM
nVidia Quadro 5000, render farmette on BB2012