So you've got something plastic with a sticker on it. You peel the sticker off and there's sticky gunk left behind...
taunting you. So what do you do about it? There's lots of suggestions out there, but are there any different ways that might work better?
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... most often clear plastics become opaque.)
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 better with each other than they do with water). And I would
definitely say for the first time using this technique, 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.
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. It also rarely works with old adhesive (that barely feels tacky anymore).
First, make sure that the item is tightly held onto a flat surface. I'd suggest - if you don't want to scratch the underside - on a soft (but not terribly thick) washcloth. ['Not thick' so there's limited flexibility to move up and down much.] Then press down tightly to hold the item with your other hand, surrounding the area you'll be working on (the less movement of the item, the less likely you'll break it if it is thin). Try an average-sticky tape (usually Scotch brand [generic adhesive 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 against it. (I usually do that with the tape wrapped over one or two fingertips, with the adjacent fingers holding the tape in place.)
You should notice bits of the adhesive coming off the item 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 you are using (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 of effort, 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 someone out of a sticky situation.

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).
Any other unique ways people have gotten sticker residue off of plastics?
[This originally came up as a topic in the Red Dawn area as a used DVD had adhesive residue on the playing surface of the disc. Since far fewer people would be likely to see this technique there than might benefit by it for general use, I figured I'd copy what I wrote here in the 'general' area and edit it a tad to describe any item, not just a DVD.]
Some specifics for CDs or DVDs with adhesive residue:
I've never had to, but if you need to use this on the playing surface of a prerecorded DVD or CD, 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 the technique on a food container - trying on a disc you don't care about (even if there's no adhesive on it). [Never use this technique with the playing surface or even the label side of a DVD-R or CD-R. The dyed layer of the playing surface may come off rendering it unusable. But I actually had the label side of a CD-R come loose just trying to remove a CD-R adhesive label, making the disc unplayable as it let air between the reflective and polycarbonate layers.]