We don't need no stinken badges here!
Get yourself the following items:
2) Waxed Dental floss (you can use mint if you really want to)
3) Rubbing Alcohol
4) Microfiber Cloth
5) Paint Sealant or Car Wax
The process is really really simple:
*** I am assuming that you start with a CLEAN, freshly washed car ***
1) [as per the previous poster's suggestion] Warm the badges with the hairdryer. You don't want to have them melting, just wave the hot air over them long enough to warm the area (15 seconds or so). Your objective here is to heat up the glue in order to help it release easier, not to melt it totally (which would damage the surrounding paint).
2) Grab a length of the dental floss and place it against the paint right up next to the badge. Gently pull the floss under the badge in order to separate the badge from the car. ** IMPORTANT: don't be afraid to leave the floss behind the badge and reheat with the hot air when it becomes hard to move the floss through the glue AND don't pull the floss away from the car as you move it, you want the floss to move against the car's paint in behind the badge**
3) When you have the badge off the car, you will find some of the double-sided sticky tape was left behind on the car's surface. This is where the Microfiber Cloth and Rubbing Alcohol come into play!
4) Generously soak a spot on the towel large enough to totally cover the glue residue and then place the soaked towel over the residue and hold there. DO NOT RUB. After about 5 or 6 seconds, you should find that the residue will easily peel off (if not, soak the towel again and hold onto the spot until it does). The rubbing alcohol will not damage the paint or clear coat, but will break down the glue! (this also works for tar and grease removal... even bugs to some extent)
5) When the residue is all gone, soak a clean area on the cloth (or use a new cloth) and then gently wipe the cloth over the area to ensure there is no remaining glue on the paint.
6) Spot wax with your favorite paint sealant or wax because the alcohol will strip off any wax you had on the car, and you will need to protect the area that was under the badge (as it didn't have wax at all)