My hands have short fingers and thus I like cloth tape on my drop handlebar. I use Renfrew brand hockey tape for my handlebar. That tape is strong and it's durable.

On one of my bikes I wanted a bit more cushioning but didn't want to increase the diameter of the handlebar by much. So, I bought a length of copper pipe insulation foam and cut it to fit the top of the handlebar from the reinforcing sleeve to the brake lever. BUT... I cut the foam insulation so that it covers JUST the top and the back of the handlebar. When the hockey tape is pulled tight the foam compresses a fair bit and when done it doesn't slip. It gives a lot more comfort when riding with my hands on the top of the handlebar.

Cheers