All three of these schematics are things I obtained from the internet. All of them are supposed to do the same thing: Make a 5vDC regulated power supply from the input of a car's 12-13vDC main power.

All of them have a 7805 regulator chip as their centerpiece. Each one is approximately the same schematic, but each one differs in the exact layout and values of the capacitors which are used. Does anyone know what the difference is among them, and why? In particular, why are the capacitor values different in each one, and what are the tradeoffs between each one of them?

Where I got each one of these schematics:
1: http://www.aaroncake.net/circuits/cdsupply.asp
2: http://www.instructables.com/id/Power-Your-Arduino-From-Your-Car/
3: http://anceop.com/?action=page&param=viewTutorial&id=78382

Note: For the first schematic image which does not contain values for the capacitors, the values in the accompanying text are:
C1 1 1000uF 25V Electrolytic Capacitor
C2 1 10uF 25V Electrolytic Capacitor
C3 1 1uF 15V Elextrolytic Capacitor
C4 1 0.1uF 15V Electrolytic Capacitor

Schematics attached.

The first link shows a 7809 (the 9 means nine-volt output). The other two are 5V outputs. I would go with the third (100uF/10uF/100nF) version here, but really anything would work --> not much ripple to filter from a 12-14VDC input from a car. If the source was AC power through some diodes, one might get fussier and read the exact parts' datasheets to get the recommended values.

EDIT: Eg, here is the datasheet for a Texas Instruments 78L05 chip. Refer to the top of page 11 for recommended capacitor values (0.33uF and 0.1uF in this case).

And here is the ST Microelectronics version, again recommending 0.33uF/0.1uF (page 2).

The further the regulator is from the source of power, the larger the first capacitor. Or at least that's what I have read in other datasheets.

Cheers!

The L78 series is a linear regulator, it's meant to regulate an output from a fairly close input voltage, not do conversion as you're doing here. It's gonna get hot.

Use something switching, like an LM2575-5.0.

What Larry said. If you don't want to roll your own, you can get something like this: DC-DC power supply. Note that they sell a nice metal enclosure for an additional $4.

There are much simpler/cheaper options on eBay for "buck" voltage convertors. Usually just a dollar or two, and they'll handle anything from 60V down to 2V over your output. No heat to speak of, even when stepping down from outrageously large inputs.

Eg. This one for a buck, delivered (slowly). Or pay a bit more on dx.com and get it within a couple of days (yes, they now have FAST delivery on a lot of stuff).

For this application, even a 7805 would actually work just fine without too much heat, because the current draw is likely to be in the milli-amps range. I have built several devices here that take 12V in through a 5V linear regulator without much fuss. I do put a small heatsink on some of them, but not all.

Cheers

Without a heatsink, the L78 will definitely be fleshsearingly hot.

I have used this sink before:

http://futurlec.com/Heatsinks/TO220SMBLpr.shtml

it keeps things merely hot. It also has holes for firmly mounting it to your pcb.

Given that this is for a car, it's best to worry about stuff like heat and vibration.

Thanks so much for all these tips, everyone!

I already purchased heatsinks to attach to the 7805's and was intending to test everything carefully to make sure that the heat wasn't a problem.

Here is a wide variety of small step down converters.
https://www.pololu.com/category/131/step-down-voltage-regulators

Typical size compared to the 7805

Or for something to deliver 2.1A buy a car usb charger, hit it with a hammer and remove the innards

I use this technique for 12V and 240V.

I do like building my own circuits but sometimes this is just so much easier

A +1 from me for a switching regulator on a module, they are so cheap it's really not worth the effort doing anything else.

As mentioned 12-5V is a fairly large step down for a linear regulator. Even 100mA will be 700mW of heat which is quite a large amount.

A car USB charger is a good idea too for up to 2A or so which would be well out of realistic range for a 7805.

Presuming this is for the BT empeg project, how much current is the BT module rated at?

I forgot to say, a while back, thank you Glenn for that link to the voltage regulators on the Pololu site. I got some there and they work well. It generates essentially no heat compared to the 7805 solution.