What Should Be On The Box?

My personal preference would be the catchy stuff on the top and front end of the box like the name and picture of the game. Maybe use a small corner for age, number of players, playtime and maybe a small company logo. Use the back to reinforce the fun. Like having a picture of game being played and bullet points or quotes. I'd put the company logo on the back and maybe the sides. As far as contents of box if it had tons of parts maybe something like "153 game pieces" or smaller "game includes: cards, dice, and board"
Game designer and specifics should be on the directions in the box.
Then again that's just my opinion.

Identifiers: Game name - Company logo - Designer's name.
Any one of these things can potentially sell a game by itself. If a game DOESN'T have a designer's name on it, my first assumption is that it probably wasn't designed, it was just thrown together (though i'll grant that that's from a very specific perspective). These are also the things that people may Google while they're in the store.

Basic Info: Play time - Number of players - Recommended age.
People shop for these things. If they're looking for a kid's game, but you don't have recommended age on it, they'll often assume you're outside their range. If they're looking for a game that runs 2 players specifically and you don't say this on the box, they'll put it back on the shelf and look for something that specifically says 2 players rather than gambling that yours does.

What cements the sale: Art for front of the box, game-in-play on the back of the box (and maybe more art), theme/gameplay blurbs.
The box will most frequently get picked up based on the art on the front. When they turn it over for more information, give it to them fast and interesting, you've only got a few seconds. If there's no realistic shot of the game, people will assume the components aren't worth showing. Having the components shot be set up as a game-in-play lets store owners do some basic "this is how this works" explaining, too.