I know some people have a different way of doing this, but I thought I'd upload an example of my solution to the problem.
After some experimenting, it seemed to me that it would be best to make a game in 4:3 ratio, and let the widescreen users put up with the stretching, which is less than you might think.
Also, rather than switching the monitor to the resolution required for the game (which can always be left as an option to the user), I experimented with stretching the game window to the users desktop resolution to fill the screen.
The uploaded cap also has a couple of performance tests, like background warp and 800 sprites, just to see if the stretching technique actually affected the speed of a game.
It runs in a borderless window 1024x768 and is stretched to match your resolution for fullscreen.