Sometimes it can be helpful to a dungeon master for a character to have a favored hand written on his character sheet. This can quickly solve some arguments which might pop up over throwing stuff while still armed, as well as some odds and ends.
Now, we both know that if we just let characters specify what hand they favor, then they will always claim to be ambidextrous, which we just can’t have. That and I love charts that allow us to use our poor and often neglected 12-sider.
Personally, I like rules that are easy enough to remember that you don’t even need a chart, so in my work-in-progress system you roll 2d6. On doubles you’re left-handed, on a 12 you’re ambidextrous. That gives results that are quite reasonable, and I can remember it off the top of my head.
I use the same method for determining sexual orientation for NPCs (or PCs that want to roll). That probably overstates the prevalence, but re-using a rule is even easier than remembering a new one!