The Raspberry Pi does not have a built in ADC, which is unhelpful if you need to read any kind of analogue value, such as a variable resistor position or a light level etc. PICAXE is a line of cheap microcontrollers, designed to be easy to use for school children. This means they are easy to use, and you may have one lying in a draw. This instructable will show you how to use one as an ADC, but by writing values to it, you could conceivably use one as a port expander at the same time.
Step 1: Set Up Pi
Step 2: Circuit
Only certain PICAXEs can act as an I2C slave, in this case I am using a 28X1. You need to build the basic operating circuit, as shown below.
Build the minimum operating circuit, of power and reset resistor, for the IC. Then, build the download socket and 2 resistors. This may not actually work on a breadboard, because the plug may not fit, so this might have to be assembled on veroboard. Finally, connect one end of each variable resistor to +, the other end to -, and connect the wiper to the ADC pins.
I have assumed some basic knowledge about PICAXEs, but if you have never used one before, I recommend reading PICAXE Manual 1 (just type it into google).