Replace '94 LX wagon head unit with an amp
 

Recently my car got broken into and the aftermarket head unit was stolen. As I never used the radio before - much less the CD player - it really wasn't a big deal at first, but now I'm getting sick of having to deal with headphones and an iPod or my phone whenever I want to listen to music in the car. Plus, it's not terribly safe, or legal for that matter.
I've been looking into the idea of buying a cheap amp with an aux jack and just wiring that into the speakers in stead of replacing the head unit. I realize buying a new head unit with aux input would probably be easier and less eccentric, but I'm kind of into doing things the non-conventional way.
Is what I'm thinking of even possible? What kind of amp do I need to buy? Has anyone seen this done before?

yes, what you want to do is not that uncommon given the rise of putting tablets into dashes - it's the same concept.

I think the JL Audio Cleansweep products are a good choice for this. You will get a 3.5mm input and a remote volume control - so you have a normal knob to use.

JL Audio CL441dsp CleanSweep® Sound processor for use when adding amps and speakers to a factory system at Crutchfield.com

then a small aftermarket amp to power the speakers. The CleanSweep will sense the audio signal and turn the amps on and off for you. any cheap amp will do - look on eBay for one used. I like older Alpine MRV for good quality, inexpensive, used amplifiers.

cheaper options

Lepai 4x45W Mini Amplifier with Remote USB MP3 Media Card FM | 310-304

Lepai LP-2020A+ Tripath Class-T Hi-Fi Audio Amp w/Power Supp | 310-300

then a remote level control through the RCA
Metra