Solvents 
   
The reason this section is important isn't just because gummy price tags are a pain in the whatsitz.  When it comes to painting and gluing, the axiom of the business is, "90% of a good paint or glue job is surface preparation."  If you're painting or gluing something and you want it to last, you need to know something about solvents.
Solvents have a certain ascending order of strength.  When attacking a fresh spot, you usually work your way up, depending upon the surface.  That is, if the surface is something tough, like glass or fiberglas, you'd start off with something stronger than if the surface is a soft plastic like plexiglas.
Overall, I find lighter fluid (naphtha) to be the best all-around solvent for things like gummy price tags.  It cuts through most things, and won't harm delicate plastic surfaces.
Here's a general order of ascending strength:
Soap — 
 Probably the mildest soap is shaving cream.  I use it to clean dirty CDs as it doesn't leave any residue.  Next up would be dish suds, then bar soap, then bar soap with pumice, like Lava.
   
409 —  
 Does a very admirable job if allowed to sit for a bit.  I once did a comparison test between 409 and Fantastik on a real greasy kitchen wall, and when sprayed and wiped immediately, they were both the same.  But when left to sit for about 20 seconds, the 409 did a far better job.
   
Release — 
 I just discovered this amazing stuff the other day.  I had removed a mirror from the fiberglas wall of the shower, and the double-sided mirror tape goo left on the wall was a hideous mess.  I hit it with all the usual stuff and never fazed it.  I then tried the four solvents I'd bought trying to find something that would dissolve 3M 5200 (the nastiest silicone-type glue of them all).  The first three didn't touch it, then I hit it with some stuff called Release, by a company called BoatLIFE, and it was like a miracle.  A few spray-and-wipes with some paper towels and the mirror tape goo was history.  I got the stuff at a marine store.
   
Alcohol — 
 Rubbing or isopropyl alcohol will cut through a few things, and it's almost guaranteed not to harm the surface.
   
Lighter Fluid — 
 I usually start with this.  You can buy cans of naphtha at the hardware store, but the Ronson lighter fluid works much better for just splashing a bit on a paper towel.  It's still available at most grocery stores.
   
Turpentine — 
 For things like price tag goo, lighter fluid will probably work 90% of the time.  If it doesn't, then that means the glue has a different 'base' and turpentine might be the answer.
   
Lacquer Thinner — 
 This is some pretty nasty stuff, so make a tiny test spot if the surface is delicate.  Evaporates quickly, so use a dense rag rather than a paper towel, and keep the place ventilated.
   
Acetone — 
 Same story as lacquer thinner.  I usually jump to this if lighter fluid fails, surface depending.
   
And a few oddballs:
   
Butane — 
 While not being a particularly good solvent, butane, like from refillable lighter canisters, has one property that none of the above do.  I was once into photography, and one day I was trying to achieve a 'soft edge' effect by smearing a little bit of Vaseline around the outside of a clear filter.  I went to clean it off later, and, no matter what I tried, everything left a tiny, tiny film on the glass.  In a fit of desperation/brilliance, I grabbed a can of butane, blasted the filter, hit it with the lens paper and voilà!
   
Carb Cleaner — 
 For petroleum-based problems, carburetor cleaner is some nasty stuff.  If you have some hardened grime or grease, give it a big blast with carb cleaner every five minutes for a while, then see what happens.
   
WD-40 — 
 Although its proper designation is 'penetrating fluid', it's basically a rust solvent.  It's to note that there are much better penetrating fluids out there than WD-40.  I use some stuff called 'PB Blaster', available at fine auto stores everywhere.
 
Warning:  I once started working for a business, and there was a piece of clear plexiglas used to prop up papers on a console.  It has some gummy residue on it, and, there not being any lighter fluid around, I jotted it down on the shopping list.  The next time I went shopping for the company, the Home Depot didn't have any lighter fluid (no surprise), so I bought some of that 'Goof-Off' I'd been seeing around for years.  I applied it to the clear plexiglas and it dissolved the plastic right before my astonished eyes.
Like soaking a sinkful of crusty dishes, solvents definitely work better if they're given time to work.  The problem in many cases is that they evaporate quickly, so there are occasionally times when it works better to use a milder solvent that doesn't evaporate as quickly, such as lighter fluid, than a more powerful solvent, like acetone, that evaporates almost instantly.