I'm going to assume watch and wallet don't count, simply because those are standard, every person carries type of thing, rather than supplemental tools specifically chosen for EDC capability enhancement.
If I had to narrow the 13 things I carry down to 3 (not counting primary folder as stated by the OP) they would be the following:
1. Leatherman Squirt PS4
2. Iphone 4gs
3. Bogota lockpicks
The first two items were a no brainer:
I've been carrying a Squirt for the last 5 years and it has handled every task imaginable, while still being small and unobtrusive. The Iphone is simply magic, and takes care of several functions such as LED light, note taking, thereby covering the loss of my flashlight, paper, and pen.
The lockpicks were my last tool simply because when I need them, no other tool will do, and they are very difficult to come across or improvise- I can skip a lighter and tape, because I could borrow those from someone else, or purchase them at a store, but you can only get the Bogota's over the internet.
