I've had success with a Scotch-Brite pad soaked with either WD-40 or Goo-Gone. Then I wipe any remaining film away with a clean rag and soapy water or solvent before re-wrapping.
+1 Been doing it this way for years and have done lots of bars. They don't have to be perfectly clean, as others have pointed out, but my anal nature insists that mine get cleaned off before new tape. And...
I never use adhesive tape anymore. Pooey-stinko! These days I buy cheap foam/cork tape from China. $2.00 a set, including shipping. Easy to apply, easy to remove and feels/looks just fine, in my opinion...
