carl1864:
ImageShack - Best place for all of your image hosting and image sharing needs , however they are also applying voltage to the AREF pin, sometimes direct, and sometimes through a resistor. Is this necessary or not? I've never used the aref pin on my duemilanove for anything.]
It is only necessary when you are going to be using analog in. It's the Analog REFerence pin. I don't know much about it but I don't use it either. Unless you know your going to use it just don't hook anything to that pin.
carl1864:
Also, some are not using a pull resistor on pin 1 reset, and others are. Is the resistor pretty important, or not really?]
If you use a switch to reset the chip then yes it is very important to make it work. If you are only unplugging/plugging power to it (or using an on/off switch) then all you need to do is wire reset to +.
The way the reset works is like this: The resistor ties reset to +. If the pin goes low (or rather has - charge instead) then it will reset the chip. When you press the reset button, the resistor stops the flow of + to reset, and - flows, thus resetting the chip.
If you do NOT wire the pin at all, then that reset pin is floating. In other words, you may be ok, but you may not. If the pin floats and get's interference of any type then it may just start resetting itself constantly.
carl1864:
And I don't get why, if the voltage regulator can by made with just the chip and 2 capacitors, why is the rbbb kit (and others) using 3 capacitors, and a diode? (plus an led, but I understand the point of that).]
The two capacitors are needed if you are going to use a voltage regulator as opposed to usb power. The diode is to ensure you don't burn your chip by connecting ground and VCC backwards.thanks to WestFW for the info
carl1864:
All the info just varies so greatly from different sources.
I hate asking so many questions, but I'm just baffled by how hard of a time I've been having finding this basic info. I've searched for "minimal", "standalone", " bare minimum", and others, and read at least 50 pages of so called minimum arduinos, and none of them are minimum. They all have tons of extra parts for programming, and generally are pretty full fledged programmable arduinos. I mean, thats good for a diy arduino that you can work on, and those are very cool. But if you already have a working project with all the bugs worked out, then it shouldn't need any extra programming. If you want to make it permanent, or make multiple permanent copies of it to give to family, or other situations like that then there is no point in wasting time and components, using anything more than the bare minimum components, and minimum connections. Seems like something 95% of the arduino users would want to do this. Make permanent minimal installations of successful projects. Yet info such as a simple accurate schematic of the bare minimum for a stable working chip, without anything extra, has been near impossible to find.
I see what you mean, and I have been there. Don't need the regulator if you are running on usb as it's regulated already, you do need the capacitors and diodes, you don't need the crystal, you don't need an led, you do need a means to connect the chip to flash the firmware, but if you have another arduino, or have an icsp programmer (also these are easily makable with a serial port and a few odds and ends) to flash the application to the chip then just do it on a breadboard before you solder.
That's pretty much it. All you need is an Atmega chip, a usb power connection, two capacitors, a diode, a power switch, 6 wires to connect these (and 1 for + to reset) and Voila! 
As soon as I get home, I will make a simple schematic in fritzing that will help you tremendously as to what parts do what, and why or why you would not need them 
Till then, lemme throw you a schematic of my chip I am setting up right now. The Atmega32L

FYI THIS schematic is adaptable if you download the fritzing file (from here: http://fritzing.org/projects/the-atmega32l-programming-the-beast/so you can see which pins on the atmega32 are what so you can adapt to those pins on the Atmega328.
Things you can leave out of my schematic though: the breadboard with the 3 leds(and all connecting pieces on that breadboard), and the two ceramic capacitors and the crystal.