So, you've just purchased a wonderful new bicycle and love everything about it - except for the gaudy decals that serve no purpose other than to make your ride a prime target for theft. Not to worry, removing them is a simple process that will take less than an hour of your time.
Step 1: Apply heat to loosen adhesive
Using a heat gun or hairdryer, apply heat to the decal to loosen the adhesive.
Step 2: Scrape away majority with a metal edge
Continue to apply heat as you scrape away the majority of the decal with a dull (not sharp!) metal edge. Use a very light touch, and scrape in one direction (not back and forth) so you're not continually pressing melted pieces back against your paint.
Step 3: Scrape away leftovers with a credit card
There will likely be small pieces of melted decal left that you won't be able to easily remove with your metal edge. To clean the rest of it off, wait for the bike to cool off a bit, then use a credit card to scrape the rest away.
Step 4: Finish with adhesive remover (if necessary)
Depending on the type of decal you encounter, it may be necessary to finish with a bit of adhesive remover. It wasn't needed for this job, but I recommend GooGone if you find the area is sticky afterward.
Enjoy the clean look of your bike without decals!