Armor all, and most other interior 'dressings' contains silicone disolates. This ingrediant is not only the equivalent to putting cooking grease in your hair to give it that 'natural healthy shine', but it's also 'addictive' for the interior of your car like a bad drug habit. In other words, when you apply it the first time, it looks great (if you like the 'glazed donut' look) once the stuff wears off, your plastic is slightly worse looking than before you even used it, so you use it again to get it looking good again. The cycle repeats with the plastic getting nastier and worse looking each time until it just starts to discolor and possibly even crack.
The easiest way to tell if a product contains silicone in it is to apply it to a piece of plastic or rubber, let it cure (give it maybe 10-15 minutes depending on how thick you layed it on), and then put a 'second coat' ontop of it. If the second coat makes it even shinier, then it has silicone in it... since silicone will 'stack' on top of dry silicone. Quality products will not 'stack' and will only appear as shiny as the first coat.
Another way to tell: silicone based products allow you to rub your finger along them and build up a thick residue (often times black, but sometimes clear). This also causes it to sometimes sling from your tires to your paint, and also gives interior plastic an often times almost permanent greasy feel.
Non-silicone based products generally give, at the most, a slightly 'wet' or slick feel that's actually usually anti-static (doesn't collect dust, unlike silicone which attracts it), but no residue will show up on your finger unless you just applied the stuff shortly before.
Good non-silicone based products are rare but can be found - mostly on the internet.
My favorite by far all around is 303 aerospace protectant. Meguires endurance (not the high-gloss version that's purple color, you want the standard version that's in the black bottle, as the purple contains silicone) is a good product for tires if you're looking for a quick fix at the store.
Zaino Bros. tire/interior dressing is another good option as well, and so is Lexol/vinylex.
Armorall, black magic, and so on all contain a whole lot of silicone.