I understand the importance of name and rank, but what good does it do for a POW’s captors to have his serial number? What could they do with it?
Also, are American soldiers supposed to give out these three pieces of information if captured by enemies who are civilians (i.e., Somali pirates, al-Qaeda terrorists, etc.?)
I have no idea about the first question, but service members who are considered hostages (ie, held by non-governmental forces) and expected to maintain the same standards as detainees (ie, prisoners of war and those held by governmental forces). Here’s the basic policy. Short version is you’re supposed to play nice but try not to give in to your captors’ demands. Don’t do propaganda for them (ie, signing statements or whatever), but don’t try and get yourself killed. You’re encouraged to try and establish a rapport with your captors by trying to establish things you have in common, like talking about your family and hobbies and stuff.
Basically, you can (and probably should) give away information which does not have the potential to be used against your own people.
The serial number could be used in negotiating with the government, as the serial number specifies exactly who the prisoner is–there are lots of soldiers with the same name.
This comes from the Third Geneva convention.
This convention of course only applies to states that have rattifed it, and the convention specifically says that the responsibility is the state’s, not the captors. Neither Somali pirates or al_Qaeda are state sponsored, or have states at all.
I think the information is designed to allow humanitarian agencies to be able to be notified and mediate access (ie exchange of letters) with the prisoners and their families - thus the three peices of information provide a unique identifier for the prisoner. (Curiously not every soldier gets a regimental or serial number. UK officers didn’t.)
I’m sure there was more than one Private John Smith in the American Army.
To add - communication with families is covered by article 8 of the third convention.
EDIT:
oops, nvm
My understanding is that one is required to provide to his captors Name, Rank, Branch of Service (which is a gimme since you’re wearing a uniform), Serial Number, and Date of Birth. This information is useful to report to the International Red Cross so they can report it to the appropriate authorities so they’ll know precisely who is a POW.
When I was stationed in the Bahamas, as part of our continuing professional education, 2 or 3 times a week we had to have training on some sort of military topic. It could be a fire drill, a lecture on how we ordered supplies, a demonstration of pyrotechnics, marlinspike seamanship, etc. Once a month the CO would put up a list of what lessons we needed to have that month and we’d each select one or two we volunteer to give. And sometimes, the less popular topics were assigned. There was a file cabinet drawer full of lesson plans for the topics we could use.
I got stuck once with “U.S. Code Of Conduct” which is about the rules we’re supposed to follow as a POW. Basically, it’s don’t narc on your fellow POWs. I started the lecture, but when the CO stepped out to use the head, I shifted the topic a bit. When he returned, he came to see the entire crew holding their hands over their heads repeatedly chanting, in unison “Tovarich! Amigo! Kamerad!”. I explained that if you’re going to become a POW, you’d better know how to surrender and I didn’t think the North Koreans or Vietnamese were going to attack a USCG LORAN station in the Bahamas, Cubans with Soviet or East German advisors were more likely.
There is a pretty heavy course you can take that I’m not going to get into but to be blunt, all of the BS you see with prisoners getting questioned and antagonizing their interrogators is simply not done.
SERE? (Survival Evasion Resistance Escape)
First thing that came to my mind. It’s not exactly a secret. It’s basically a course of brutalization and coercion designed to break you. I was glad to have missed it. The military was eager at that time to get people to Vietnam, so after I finished the military training portion (basically weapons familiarization), they announced that all E-4 and above would be going to SERE and the rest of us would be deploying. Score!
No. Not SERE, but that’s a good course too. Not even ASERE
Funny story, Warrant Officer friend of mine keeps trying to convince me to take ASERE (Advanced). He says, “Come on, it will be fun!” He’s an instructor.
Fun for who? Ha! Not me!
Something non-military types may not always get, military folks like to try and suck their buddies into horrible, bag-drive courses for “fun”.
If you get suckered into holding the bag on a snipe hunt, you’re certainly going to see if can sucker the next guy.
Or searching for a box of grid-squares. 
thankfully never fell for any of them, and also didn’t ask to be loaded onto ASERE.
What’s so hard about that? I’ve got a box full of grid squares in my closet.
After hearing other guys’ tales of SERE, I was really glad to have missed that little picnic. Being folded into a box until you’re screaming or being nearly completely submerged in a barrel full of slime and only allowed to breath through your nose would have freaked me right the fuck out. I always thought I’d make a lousy POW.
Is it next to the gallon of prop wash? Can I borrow a few yards of flight line?
Plus, if you got conned into signing for The Suck (a.k.a. military life), you’re obviously an impressionable and likely lad.
IOW, a complete sucker.
I just caught a sea bat. It’s in this box. You mean you’ve never seen a sea bat? 
I have a can of radar grease, if you want to come get it. I also have a small stash of backblast repellent, but you’d better hurry.