I just picked up a Pioneer receiver with some speakers. If I wanted to run a single 10" woofer, would I need an amp? I feel like I can get away without one.
Like josh said you would only be getting the output from the headunit which is rated near 40 watts per channel I believe. Get an amp even if its a cheapo it will be better than running it off the headunit.
If you didn't use an amp, it wouldn't sound worse with a sub than without. If you don't get an amp, skip the sub. And ditto on the Mach system, I've been wanting to get rid of it but dreading the wiring since I bought mine 2 years ago.
I didn't feel like pulling the amp under the radio in the center console, so I just left it there. But if your starting from scratch, it's really not too bad if you just take your time. I pulled all the seats and carpeting out of the way. I got my pioneer head unit from Crutchfield so it came with the wiring adapter etc. and that made wiring the pioneer real easy. I opted to run new speaker wires since I added an amp for the component speakers and a sub amp to power my dual 10"subs and the amp wiring kit came with speaker wires.
SOme Pioneer decks have the ability to bridge their rear channels and run a 2ohm load for a small sub. I ran one like that in a Jeep I had powering an 8" Bazooka. It worked fairly well.