We are big on recycling, but reusing jars with labels that won't come off doesn't always work for us. We found that peanut butter can get the sticky adhesive off of jars with no issues. Fast and effective.
It doesn't seem to matter what kind of peanut butter you use, so stick with the cheap stuff for this.
Step 1: Peel
Peel off as much of the label as you can.
Step 2: Soak
Soak the jars for in hot soapy water for a few minutes and see if you can peel more of the label off. This step is kind of optional, you don't have to soak the labels I just think it reduces the amount of peanut butter you use.
Step 3: Peanut Butter
Cover the label/sticky area with peanut butter and let it sit for a few minutes.
Step 4: Wash
Paper towel or a sponge will help you with scrubbing around the sticky areas. Rinse with hot water and dish soap.
Step 5: Dry
Dry your jars and then they'll be ready to use.