Loads of good advice, all.

The biggest mistakes I see made with bar wrap are poor tension and uneven spacing, both of which can be corrected with practice by most anybody.

My favorite tapes are bike ribbon:



...and cotton:



I enjoy wrapping them all, but the ribbon and the cloth seem to just lay nicer. Bike ribbon has those nice thin edges that rest in the valleys when you wrap it nice and tight. Cotton tape shows the layer underneath with each rotation - a look I really appreciate. And with cotton, there are multiple ways of finishing it off nicely. I prefer a bottom-up wrap and hot glued ends. On the one pictured above, I took the French flag ribbon that came on a Christmas gift - a cocotte - and applied it to my tape, hot gluing it out of sight.