How do I get leftover tape stickiness off of plastic surfaces?
Okay...there's kind of a long story behind it, but I have left-over stickiness on the front of my alarm clock because it was bright, and I didn't notice a switch on it. It's from scotch tape that's been removed, and it's making the alarm clock rather hard to read.
I've tried cleaning it with a wet cloth, but it wouldn't get it off. I also tried scrapping it off with various things, but I couldn't get stuff flat enough so it only took off little strips. (Some things took off some of the alarm clock's plastic too...)
Any tips would be appreciated, and the easier/cheaper, the better. 
Goo Gone! - they claim that it's safe on any surface, and I haven't used it anywhere that it's caused damage, but check a small spot first just to be safe.
If you want to try something cheap, you could always simply get the stickiness off with more tape, but that probably won't work with old grungy remains.
WD-40 works really well for this also.
I suggest a white eraser. Just rub it and the glue will warm up just enough to stick to the eraser "shavings". (Works well on CDs, books, etc.)
I always use turpentine. I've tried a bunch of others things but for me turpentine works best and fastest.
I have used De-Solv-It to remove a lot of sticky substances. As previously mentioned, Goo Gone works well too.
Cheap and easy is plain old vegetable oil. You need to let sit for a while so that the oil penetrates the glue.
Almost any citrus based cleaner will remove glue traces. The stronger the concentration the better. It will not wreck the plastic like some harsher chemicals will.
Peanut Butter
I use it to remove the label residue from glass jars. Just smother it all over, let it sit for a while, come back and wipe off.
I use lighter fluid and a paper towel. Works great!
nail polish remover works perfectly!
Remove Sticky Tape Residue & Glue | Clean Sticker Adhesive Super Easy | Strong DIY Cleaner