If there's more than 1 or 2 words in the ingredients that aren't actual food, I usually don't buy it.
Instant no's are partially hydrogenated anything, HFCS (or even just regular corn syrup), MSG.
I'm also convinced that sodium benzoate is no good. I went for about 3 months one time where I did not eat one single processed food item, and when I had some food with preservative in it (sodium benzoate in particular) it made me feel pretty crummy.
Oh, I also try to not buy anything with ester of wood rosin or brominated vegetable oil. These ingredients are found mainly in citrus-flavored drinks, as they make the citrus oils disperse evenly in the water. They sound creepy to me, though.
We try to stay away from all partially hydrogenated oils, artificial colors, artificial flavors, vanillin (artificial), high fructose corn syrup, all artificial sugars (aspartame, splenda, etc. . .), anything that says enriched (like pp said they have removed all the good stuff then added it back in artificially), like a pp said anything I can't pronounce or I don't know what it is I try to stay away from it because I feel it can't be natural or good for my body. We also try to stay away from soy products that don't say they are GMO free.