Get an old knife that you don't care about or a razor blade (I found an old, non-serrated steak knife worked best) and peel the stickers off. This will leave behind a residue. I used goo-gone to get rid of the sticker adhesive.
Then a green scrubbie with Bar Keeper's Friend (can be found in most groceries in the scouring powder section) and some elbow grease.
Items to keep in mind:
After you clean up the outsides you'll need to clean the keg again and get rid of every tiny bit of goo-gone and BKF and make it all clean and pure again.
The black rubber foot and handle may mark up your white tub or even your stainless steel sink. Be prepared to spend time scrubbing the sink/tub after you get done cleaning your keg.
If possible do the scrubbing outdoors-- it's lots easier if youdont' have to worry about getting water on the floor or degreaser in your SWMBO's loofa.
Take advantage of this time to do a comeplete teaerdown of your keg. Disassemble it to it's smallest components, inspeat the seals and seams and generally ensure that the keg is in top shape.
To put a final polish on the keg once it is as cleaned up as you want it: rinse the keg down, take a damp bar rag/cloth and put an ample amount of BKF on it, rub the keg in a systematic fashion from top to bottom. Makes it pretty shiney.
I bought
stickers for my kegs. Not only do they look good but I generally used them to cover up the original owner's 'property of' stamp. You can find my review of the sticekrs I bought
here.
Personally I think that a clean exterior of your keg isnt' required but when you haul them to parties and events, not only does a clean appearance make people feel better abotu trying yoru beer (after all if the outside is all scummy, why would they believe the inside wasn't) but the label ensures that my kegs don't end up in someone else's collection.
Just my experience.