Is it possible to use a wav file to send data to and arduino over serial?

What I'm asking is could you make a wav (or audio in general) file that plays on an ipod or mp3 player which if you were to connect the two leads from a mono 3.5 mm jack to the arduino's serial input you could actually send data that way?

Yes and No. The serial input connects to a harware UART that expects digital data in a certain format. From a 0 state, the data will go to 1 state for 1 bit-length of time to indicate the start of a byte, then 0 or 1 as needed for 8 data bits, then 0-state for 1 bit-length of time for a stop bit, then I think 1 more 0-state for Idle, then the next byte starts.

Audio in general is a continuously varying signal from -1V to +1V (line level output).

It is possible to send data that way. An old storage method used audio cassette tapes to record the digital data for storage, and bring it back via some circtuitry that would digitize the audio. Data speed was limited. You could play the tapes and hear this awful screeching sound as the high & lows assualted your speakers. In college classes in the early 80's, we would key in our assembly programs, and store them on tape. In the later 80's we did the same with a RadioShack TRS-80 programmed in basically BASIC for the programs used to run a simple test station.

Audio output sampled via the ADC input could be probably be captured & converted to digital the same way. Bring the +/-1V signal thru a capacitor to a couple of resistors from between +5 and Gnd so the analog level sat at 2.5V, then anything that went below ~2V would be a 0-state, and anything above ~3V would be a high state.

Check the Playground, might even be something there on it.