(my answer migrated from electronics-exchange)
Through 2" thick wood: Also tough, but not impossible. I assume you mean distinguishing between a finger/hand touching the box, and a finger/hand placed 1mm away from the box.
If you can place one or more metal plates on the outside of the box — not providing a total covering of the entire box! — then there are a number of possibilities using electromagnetic fields. I can think of a few (no guarantee that either would work!). Put your thinking cap on, and imagine how the touch of a person's skin can alter an electromagnetic circuit network.
The biggest thing that can make a difference is whether you can bring a conductor out from the inside of a box, through the wall, and connected to earth ground, or to a metal plate on the outside of the box.
1) The resistance of a person's skin can close an electric circuit -- Have two semicircular plates, separated by a small gap. The impedance between the plates is a very large resistance in parallel with a small capacitance. If you bridge the gap between the plates with your skin, you drastically reduce that resistance. If you can somehow measure that resistance, you're done:
If you can connect wires through the box walls to the plates, that's easy, just use a voltage divider and a source of DC or AC voltage that is small (don't hurt the person).
If you can't connect wires through the box walls to the plates, you might still be able to distinguish touch vs. no touch, but it'll be tougher. Maybe have another pair of plates, this time on the inside of the box, on the other side of the box wall from the first pair of plates, but with a much larger gap. Measure the capacitance between the inner plates. There may be a large enough change in the capacitance between the two inner plates with / without a person bridging the gap on the outside, that you could distinguish. There are a number of techniques/chips that can do capacitive sensing. Cypress has CapSense, Atmel has QTouch, ST Micro has S-Touch, etc.
2) A person's body is a reasonably good antenna and will pick up noise. (Look at an oscilloscope probe when you touch the tip with your finger.) If you have a plate on the outside of the box, and you touch it, you transfer that noise to the plate's electric potential. Think of this case as a person "shaking" electric potential up and down. If you can sense this shaking relative to a reference potential, you've got a sensor. The problem here is that finding a reference potential is touch. You really need a connection to earth ground, since a box floating in the air doesn't have access to a fixed reference voltage. You might be able to sense the differential voltage between two plates... dunno though.
Just my two cents.