Here's one answer I found elsewhere to the same question:
Mountain bikes use less psi than road bikes, so you'll have more leeway for different kinds of tape if it's a mountain bike. True rim tape is fiber reinforced for high psi, and also holds up well over the years (which is where most substitutes end up deteriorating). Any bike shop should have rim tape for a few dollars per wheel. Either way, make sure your tape width is sufficient to cover all the spoke holes and extend beyond them several mm to the sides.
For road bikes I'd always use velox cloth tape.Costs about a pound per wheel, fit it, forget it. Other tapes seem to move about, or not take the pressure - either way, you get a rash of punctures.
Just my 2p worth...
Never had any problems when I was riding tourers or MTBs with low pressure tyres, but as soon as I went over to HP tyres on the road bikes, repeat punctures were a problem. When I had a puncture when the wheel was hanging on a wall hook I started to get a bit annoyed and the people at The Other Place put me onto Velox. Fitted to all my bikes and no problems in the three years since. Before I managed to find an LBS stocking the Velox, I did try the Continental rim tape which is a more rigid plastic, but the edges tended to roll up and snag the tubes. Found it worse than the cr@ppy original tape.
I've been using that stiff plastic stuff - not adhesive, can't remember what it's called. Never had any problems with it provided it's the correct width and properly installed.
Beware of rim tape that's too narrow: I've had problems with two complete new bikes straight out of the shop (both, Bianchi road bikes, as it happens), on which, on cheapish double-walled rims with large, un-ferruled spoke holes, the tape was too narrow to cover the width of the holes! Result: mayhem. I believe Bianchi have sorted that particular problem, now.
My son melted his plastic rim tape and fused the tube to the rim on a long Pyrenean descent (losts of rear wheel braking) - the resulting mess had to be hacked off with a screwdriver, but it could have been worse if the tube had failed at speed. I only use Velox now.
I have only had problems when I have used insulating tape as a substitute for rim tape -always use velox - however is there another thiner type that is as good ?- very difficult to get tyres on and off and I thought i would try a thinner tape - but no good if its not effective