This should be simple, but for some reasons I am having trouble coming up with a solution.
Essentially I have a structure which contains 2 2D vectors (coordinate and size). I have about 20 instances of this structure. I also have a grid. What I want to do is randomly set the coordinates and sizes of these 20 structures so that they all fit into the grid and do not overlap each other.

The problem is that I need to have all of them in there. If I just start tossing them in randomly, its possible for one to become too big and take up the entire grid, which prevents others from forming, causing an infinite loop right in the beginning of my program (which sucks). I also want to minimize the possibility of very very small rectangles, since that could make it too easy for the player of my game (winning could consist of eliminating a specific rectangle).

Any ideas?

If you want the union of all the rectangles to be a big rectangle, perhaps it's easier to start at the top. Take a big rectangle and subdivide it into two rectangles, by cutting it in two by a random line (perhaps along the longest side). Repeat until you have 20 rectangles. This procedure always results in tilings that have "fault lines", but that might be acceptable in your application.

The simplest way I can think of (that I've personally used in the past) is to use Binary Space Partition - where you split the rectangle down recusively until you have the desired number of sub rectangles.

This describes the method as used in procedurally generating a 2d dungeon:
http://roguebasin.roguelikedevelopment.org/index.php?title=Basic_BSP_Dungeon_generation

The simplest way I can think of (that I've personally used in the past) is to use Binary Space Partition - where you split the rectangle down recusively until you have the desired number of sub rectangles.

This describes the method as used in procedurally generating a 2d dungeon:
http://roguebasin.ro...geon_generation

If you want the union of all the rectangles to be a big rectangle, perhaps it's easier to start at the top. Take a big rectangle and subdivide it into two rectangles, by cutting it in two by a random line (perhaps along the longest side). Repeat until you have 20 rectangles. This procedure always results in tilings that have "fault lines", but that might be acceptable in your application.

Ok, great, thanks. This solves most of my problems. I may use this kind of algorithm, although I am not entirely sure yet. I do want there to be some space that remains outside of any rectangles (the player's starting location), but that can be accomplished manually.
The more I think about the problem, the more complicated it seems. I will try to use BSP and see what the result looks like. It solves many of the problems: all rectangles will fit, none will be too small, and it prevents overlapping.
The cons are that it isn't quite as random as I hoped; for instance, there is always a big line down the middle.
The rectangles will represent the territories of in-game rivaling factions. So the borders will be danger zones where factions conflict, and border shapes might change depending on who wins the conflicts. So what I can maybe do is use BSP to divide, and then simulate some conflicts to randomize a little more, although that runs the risk of eliminating factions before the player even gets a chance to play, although it would be very rare and I'm sure I can find a way to prevent it completely.