A lot of action figures come in packaging called a blister bubble (this is also what a lot of pills come in, but they're usually a lot easier to open). When you tear off the cardboard backing, a layer of it remains stuck to the plastic bubble. Now you gave to get a pair of scissors to poke a whole through the cardboard so that you can extract your Star Wars character and play with it. Hopefully you don't accidentally cut off its saber-arm.
Here's another shot of the same phenomenon, this time with a package of floss. Doesn't that annoy you?
How about this bottle of vitamins. What were they thinking? Two tamper-evident seals? You just know there's an evil genius, somewhere, cackling every time someone opens one of these only to discover that they have to do it again.
A close runner-up to the worst packaging ever is the wrapping on CDs and DVDs. First of all, they usually pack the plastic so tight that you can't even get a fingernail under it. Once you have the plastic wrapper off (and it doesn't always come all the way off, like on the spine of my copy of The Truman Show), then you have to deal with the obnoxious sticker strips that they stick on three of four edges. This is done to prevent people from copying the CD or DVD and then returning it. But does it really need to be impossible for the legitimate consumer to remove? Sometimes you have to mutilate the case just to get the darn thing off (like Leann did to her 10 Minute Solution Carb Burner).
The worst, however, in my opinion, is the two pieces of plastic stuck (riveted?) together (shown above), which usually contain electronics (or, in this case, tools). It looks like you should be able to pry the two pieces apart and your purchased product will simply pop out. Not so. The jaws of life couldn't open this puppy. You're going to have to do extensive surgery on this thing with a sharp pair of scissors before it will relinquish its contents. Even then, it might not.
 It is my understanding (though I don't recall where I got the information nor can I corroborate it) that tamper-resistant lids were first developed for bottles of baby food in the 1950s to prevent mothers from sticking their fingers in, tasting them, and then putting them back on the shelf where they would spoil. If someone else bought it, it could potentially harm their infant. And if no one bought it, that was a loss for the store and/or producer of the baby food.
 I wonder if there are people out there who take one vitamin and then stop because the side of the bottle says "Do not use if seal under lid is broken." There's gotta be a "Yo' Momma…" joke about that.