How do I create block diagrams in Microsoft Office without using Visio?

You can use SmartArt or Shapes in Excel. Just go to the Insert tab and click on SmartArt or Shapes. It's not as easy as Visio makes it, but you can still do it.

BTW, SmartArt is annoying to use for the kind of flow chart you want to create. I would recommend the regular Shapes.

Example:

EDIT: Forgot to mention that you can pretty much do this in Word and PowerPoint.