I joked about Chris' pencil & paper suggestion, but it is certainly way superior to the native facilities in Word & Excel!
I would rather use a pencil & paper and then scan the result than use the native facilities in Word or Excel!!

But the one big, vital difference between Visio and all the other drawing packages is the way that it knows about connections - which is essential for any sort of interconnection diagram like State Diagrams, Data-Flow Diagrams, Flowcharts, Structure Charts, etc, etc

With all the other drawing packages, you can draw a box, then another box, then a line connecting the two - but if you want to move one of the boxes, you then have to also move the line; with Visio, because it knows about connections, you just move the box and the connection automatically stays with it!

The only other way you'll get this is with a full-blown CASE tool which will be far more expensive, and a lot less versatile.

Oh, did I mention that I like Visio?