Inexpensive Force Sensors

The obvious answer is to use strain gauges. They can be had for <$10 a piece in large quantities.

If you have the time to be creative, build a parallel plate capacitor into the mechanical system. Keep the plates big and the gap small. Chances are, there will be deflection caused by the load. Build your capacitor so that the distance between plates changes from this deflection. This way, the capacitance is a function of the load (although nonlinearly).

Next, you will have to design a circuit to measure the capacitance. The simplest incarnation can be just an RC oscillator with a few BJTs ($0.10) but it is not very temperature stable. There is no end to how fancy you can make your capacitance measurement device. Cost is your trade off there.

@yyao: Super cool concept, I've only worked with resistive strain gauges, probably due to their linearity as you've noted. @TimMontague: I am familiar with resistive strain gauges, and to get a cheap-ish but still reasonably accurate (and linear) force measurement, you can start with some I found at Digikey: http://www.digikey.ca/product-search/en/sensors-transducers/strain-gages/1967323?k=sensor There are a handful there are under $20. Those seem reasonable if the fixturing is designed such that the strain gauge easily affixed to it. Then, a simple differential amplifier would do from there. I recommend an instrumentation amplifier (a type of IC differential amplifier with very high CMRR without many external components). Be sure that the one you choose has an offset so you can trim out any residual strain in the fixture (like tarring a scale). Your bandwidth requirements are likely quite low so you shouldn't have any problem finding one with an adequate bandwidth.