Okay, I just popped in my copy of Red Dawn that I aquired from ebay. And lo and behold, there's abunch of sticky gunk on the widescreen side of the disc. Now, I can contract the original seller, maybe get my money back and wait another week or two to get another copy, or I can just ask. What's the easiest way to clean off sticker residue from a disc.
Right now I'm watching it in Full Frame. Ugh.
First, as you are likely well aware,
never use a solvent that is clearly carbon-based (aromatic) on anything plastic. (It'll slightly melt most plastics and distort their surface.)
Try doing any cleaning in increasing 'intensity', starting with the least-damaging. However, there's a caveat to that: the way I've found to get adhesive residue off generally won't work if you've tried something else first.

My technique I've never actually heard of anywhere else, but came up with thinking about chemistry, mechanics and like that. 'Like merges with like' (e.g. oils mix well together, while they don't mix with water). And I would
definitely say for the first time, try practicing on something that you don't care about (e.g. a plastic container food came in that has adhesive residue left on it), just so you get used to it. Also, I have never had to do this to a DVD or CD, so I do not know if there might be an unexpected reaction between the layers of the disc (with the pressure/pulling). So I'd also suggest - after you try on a food container - trying on a disc you don't care about (even if there's no adhesive on it).
The thing that I've found to be best for removing sticker adhesive from a non-porous, hard surface is actually more tape. [It won't work it there's any paper left on the adhesive however, so try to carefully get that with a fingernail.]
First, make sure that the disc is tightly held onto a flat surface. I'd suggest - so as not to adversely scratch the underside - on a soft (but not terribly thick) washcloth. ['Not thick' so it won't move up and down much.] Then press down tightly to hold the disc with your other hand, surrounding the area you'll be working on (the less movement of the disc, the less likely you'll break it). Try an average-sticky tape (usually Scotch brand [generic quality is too uneven]), and repeatedly press it onto the residue fairly hard and pull it off again quickly so your fingers are almost 'bouncing' or slightly rolling. (I usually do that with the tape wrapped over one or two fingers, with the adjacent fingers holding the tape in place.)
You should notice bits of the adhesive coming off onto the tape. If not much 'moves', then try the next step up in intensity: try 'smearing' the adhesive side of the tape over the residue. This does two or three things, it moves the residue around which 'coats' the residue (that isn't coming up on its own) with the same adhesive that is on the tape (when adhesive of the same type easily lifts itself off), it also starts to get the residue moving which presents 'new' surfaces to stick (where what had been 'on top' might have gotten dusty or dirty, so less likely to grab the adhesive on your tape). Please note: partway through this it may look a LOT worse than it did, as you now have more adhesive than you started with. But generally that will come up easily with a second (or third, or fourth) piece of tape. It may take a bit, so be patient.
If it doesn't work with Scotch paper tape, try clear packing tape. It's adhesive is stronger than Scotch paper tape. But again start with the lesser technique and work up (in other words: start with just pressing and lifting the packing tape, and only if that doesn't work shift to the smearing).
I hope this helps. In most every instance I've tried this it has worked. The only times it hasn't are when the adhesive is of the 'permanent' type. If this doesn't work, at worst you have the same adhesive you started with smeared somewhat (as the adhesive you'd have wiped on to the disc would still have come off fairly easily).
EDIT: Though not relevant to the original problem, I would say
never try this with a DVD-R playing surface, as I would be afraid that the top (dyed) layer would be likely to come off.
Later EDIT: There is actually a second way that I figured out and have successfully used that I've never heard anyone else ever mention. Again (as you'll see) this one only works with non-porous materials. I tend to use this with those petroleum-based sticker adhesives that have dried out a bit (so are resistant to the above technique), but it will also work with things that the above tape method didn't work with. It originated, again, in the 'oil-mixes-with-oil' thought processes.
Take hand lotion, the greasier-feeling the better, and put a gob of it on the dried sticker residue. Let it soak in to the adhesive residue for a while, even overnight. Then try wiping it off with a soft cloth. It may come off with no problem. But if it only comes off a little, it may have only partially worked its way in to the adhesive, so you may need to try again, adding more lotion as it dries out. But if the adhesive shows no sign of softening or coming off after hours of soaking on the first attempt, it likely won't work at all. Then wash with soap and water to get the lotion off.
I suspect that other related dense liquids might also work with this technique... heck, you could probably try WD40 (tho not as environmentally friendly).