The technique will vary by the type of surface that you are trying to clean. Here are tips on removing tape residue from common surfaces.
If the surface is wood, it is important not to scrape or else you risk damaging the wood finish. Apply some vegetable oil to the adhesive and leave it there for 30 minutes. Wipe off with a clean towel. Then, mix a cups of white vinegar with a teaspoon of dishwashing liquid, and put that in a spray bottle. Spray the surface to clean off the oil. Dry immediately with a towel.
On painted wood, spray on the oil, wipe off excess, and leave it on for just 15 minutes. If there are still traces of it, use rubbing alcohol to remove the rest. Then, wash your wall with a mixture of dishwashing and white vinegar.
To remove reside from fabric, spray it with some hairspray and work it into the material. Rinse with cold water. Don't use hot water to wash or else the heat might set the adhesive in more.
The oil is effective on plastic and glass surfaces as well. Some people reported success using peanut butter. You can also finish off with a little bit of alcohol.
More suggestions can be found here,