In Brawl there are special items that look like white domes that activate when you pick them up, summoning a character from another game to fight for you for a short time, sort of like Pokemon.
Is there a list of these, what games they are from, and what their abilities are?
In particular, I'm interested in the background of one that shoots out a large green hand horizontally, which can push players off the level. What universe is this character from, what's his name, etc.?
These are called "assist trophies". There's a list of the ones in SSBB here: http://www.serebii.net/ssbb/assist.shtml
The one you're asking about specifically is Isaac from Golden Sun.
There is an in-game list of these, but that one you have to build yourself. The "Trophies" you collect in-game, they can be sorted in a method that groups all of the Assist Trophies together. It includes descriptions of who the character is, some minor points on their abilities in-game, and also includes one or more games which they were present in.
You can find an online listing on the official Super Smash Brothers Website over here. Saves you the time of collecting trophies, naturally.
As mentioned by Chad Birch, the character in question is Isaac from Golden Sun.
There is also an in-game list of these assist trophy characters after you complete either all-star mode or classic mode, though briefly showing those that you have unlocked.
