user213: Presumably, one powers an Arduino board with car batteries for long-term operation away from the power grid.
How can this be done, and what are the most (1) economic, and (2) reliable ways to do this? Specifically, do any additional risks to short the board with an extraneous discharge exist?

user1192: Standard car batteries are 12.6 volts there are 6 2.1V cells.  AGM batteries (i.e. Optima batteries, some interstates, and many other brands make AGM), in my experience with AGM batteries they are around 12.8 volts (I do not know the technical voltage).  Without the car running you do not need to worry about voltage spikes AS LONG AS THE WIRES TO AND FROM THE BATTERY ARE SHORT.  When the car is running the serpentine belt turns the alternator which is an AC generator.  The alternator is connected to a rectifier to change it back to DC and the unit has a voltage regulator.  When the car is running the alternator runs the electrical system and charges the battery.  When you connect to the battery while the car is running you are actually connected to the alternator.  When connected to the alternator there is a ton of electrical noise, voltage spikes, etc.
I have always had success connecting straight from the battery to the Arduino through its barrel jack connector, I have not tried any analog read function when the car is running.  On the Arduino website it recommends 7-12V, however the limits (as listed on the Arduino website below the recommended) are 6-20. I have actually experienced problems with lower input voltages.  If you feel uncomfortable just buy a 5 volt regulator and power through the usb.  

user213: There is also the higher-end Akafugu breadboard power supply - takes input from 7V all the way to 35V, but costs 11$ apiece in the bargain.

Akafugu

user562: "Practical Arduino book" has a very interesting circuit for this purpose: http://www.practicalarduino.com/projects/vehicle-telemetry-platform
Here is how I've recreated it:

It uses LM2940CT and huge electrolytic cap - even if supply voltage drops, you'll have about a second to shut down your Arduino gracefully (close files on SD properly, and so on).
"Arduino Cookbook" (2nd ed.) has a chapter with examples on how to reduce Arduino's power consumption to absolute minimum - have a look at it, too.

user213: Two more options - battery pack with convenient pre-made screw holes for Arduino, Raspberry.PI, and Beagle Board:

Smart Power Base
Kicking it up a notch - using a cordless drill's 18V battery.  The project is meant for R.PI, but it would work just as well on Arduino, as the power supply is USB

Portable PI Power

user168: I'm a big fan of USB car chargers for things like this, or USB buck converter boards that you get from ebay.

user470: Use a switching regulator such as the LM2596. You can get a ready board from eBay for about US$1.

Just set the output voltage to 5 V and feed the Vcc input of Arduino; this bypasses the onboard regulator.
The benefit is that unlike the linear onboard regulator, a switching regulator is very efficient which means less consumption and less generated heat on the regulator. An additional benefit is that it can withstand a higher input voltage (about 35 V for the specified regulator), just in case the circuit is used in a vehicle that has 24 V batteries.
The regulator has already several protections like for short circuiting, overheating, etc.

213: <p>Presumably, one powers an Arduino board with car batteries for long-term operation away from the power grid.</p>

<p>How can this be done, and what are the most (1) economic, and (2) reliable ways to do this? Specifically, do any additional risks to short the board with an extraneous discharge exist?</p>
 1192: <p>Standard car batteries are 12.6 volts there are 6 2.1V cells.  AGM batteries (i.e. Optima batteries, some interstates, and many other brands make AGM), in my experience with AGM batteries they are around 12.8 volts (I do not know the technical voltage).  Without the car running you do not need to worry about voltage spikes <strong>AS LONG AS THE WIRES TO AND FROM THE BATTERY ARE SHORT</strong>.  When the car is running the serpentine belt turns the alternator which is an AC generator.  The alternator is connected to a rectifier to change it back to DC and the unit has a voltage regulator.  When the car is running the alternator runs the electrical system and charges the battery.  When you connect to the battery while the car is running you are actually connected to the alternator.  When connected to the alternator there is a ton of electrical noise, voltage spikes, etc.</p>

<p>I have always had success connecting straight from the battery to the Arduino through its barrel jack connector, I have not tried any analog read function when the car is running.  On the Arduino website it recommends 7-12V, however the limits (as listed on the Arduino website below the recommended) are 6-20. I have actually experienced problems with lower input voltages.  If you feel uncomfortable just buy a 5 volt regulator and power through the usb.  </p>
 213: <p>There is also the higher-end Akafugu breadboard power supply - takes input from 7V all the way to 35V, but costs 11$ apiece in the bargain.</p>

<p><img src="https://i.stack.imgur.com/IB0rt.jpg" alt="enter image description here"></p>

<p><a href="http://store.akafugu.jp/products/30" rel="nofollow noreferrer">Akafugu</a></p>
 562: <p>"Practical Arduino book" has a very interesting circuit for this purpose: <a href="http://www.practicalarduino.com/projects/vehicle-telemetry-platform" rel="nofollow noreferrer">http://www.practicalarduino.com/projects/vehicle-telemetry-platform</a></p>

<p>Here is how I've recreated it:</p>

<p><a href="http://arduino.bougakov.com/post/44802340184/ok-enough-with-preparations-lets-make-some-real" rel="nofollow noreferrer"><img src="https://25.media.tumblr.com/8c2d23c56eb465d055e4d8c8406017c8/tumblr_mjb5327Gzh1s6jcaao1_1280.png" /></a></p>

<p>It uses LM2940CT and huge electrolytic cap - even if supply voltage drops, you'll have about a second to shut down your Arduino gracefully (close files on SD properly, and so on).</p>

<p>"Arduino Cookbook" (2nd ed.) has a chapter with examples on how to reduce Arduino's power consumption to absolute minimum - have a look at it, too.</p>
 213: <p>Two more options - battery pack with convenient pre-made screw holes for Arduino, Raspberry.PI, and Beagle Board:</p>

<p><img src="https://i.stack.imgur.com/T0aHD.jpg" alt="Smart Power Base"></p>

<p><a href="http://www.makershed.com/product_p/mkmts01.htm" rel="nofollow noreferrer">Smart Power Base</a></p>

<p>Kicking it up a notch - using a cordless drill's 18V battery.  The project is meant for R.PI, but it would work just as well on Arduino, as the power supply is USB</p>

<p><img src="https://i.stack.imgur.com/I9ct9.jpg" alt="Portable PI Power"></p>

<p><a href="http://makezine.com/projects/portable-pi-power-raspbery-pi-to-go/" rel="nofollow noreferrer">Portable PI Power</a></p>
 168: <p>I'm a big fan of USB car chargers for things like this, or USB buck converter boards that you get from ebay.</p>
 470: <p>Use a switching regulator such as the <a href="http://www.ti.com/product/lm2596" rel="noreferrer">LM2596</a>. You can get a ready board from <a href="http://en.wikipedia.org/wiki/EBay" rel="noreferrer">eBay</a> for about US$1.</p>

<p><img src="https://i.stack.imgur.com/HyLG8.jpg" alt="Enter image description here"></p>

<p>Just set the output voltage to 5&nbsp;V and feed the V<sub>cc</sub> input of Arduino; this bypasses the onboard regulator.</p>

<p>The benefit is that unlike the linear onboard regulator, a switching regulator is very efficient which means less consumption and less generated heat on the regulator. An additional benefit is that it can withstand a higher input voltage (about 35&nbsp;V for the specified regulator), just in case the circuit is used in a vehicle that has 24&nbsp;V batteries.</p>

<p>The regulator has already several protections like for <a href="https://en.wikipedia.org/wiki/Short_circuit" rel="noreferrer">short circuiting</a>, overheating, etc.</p>
