I've just bought a new Blackberry Pearl through my US provider (AT&T) but will be abroad for the next year in South America. I've heard a lot about unlocking phones for use with other (foreign, in this case) providers and would like to explore this option a little bit more. I would just like those in the know to weigh in on this--should I try paying for a code through on of the many online services, buy one through Ebay, or try my luck asking AT&T to do it? Any advice is appreciated.

Right I only deal with Nokia's personally, so not 100% about other brands, but that said it does seem yours is possible to unlock, but the best method for you will depend on your sp (service provider), some are real jobs worths, others are as good as gold, many a time it will depend on the person you talk to, hence not being able to say specifically whats best for you.
There are 2 options for you, first is your sp, this is best "IF" they play nice, my hope is that if you tell them your going abroad and can't use they're service there (need to know your phones operating frequency's) that they would then give you the code for free, BUT, if you are tied into a contract or have any obligations to fulfil with them, odds on they wont help, not unless you pay whatever your obligation is to them.

The other possible is to find a friendly assistant in one of their shops, see if they will help, might be easier in person, failing that your reduced to a 3rd party solution there are many such people around, but some are right cowboys so only use one thats trusted, and when entering ANY code, make sure you only do it ONCE, if it fails you only get 5 chances in total before the phone can only be unlocked via hardware only, so do not guess at these things.

Here is a trusted place, I help run the forum that owner has, and I have followed him for near 20 years now, and I've yet to see any complaint about him, I don't get a penny so don't think I'm suggesting them because I get something, I suggest them because I know the service is great, nothing more, but you can go anywhere you like, just make sure to check them out before parting with money, because there are many who will take the money and laugh if it goes wrong.

Now, I mentioned frequency's above, you need to know what frequency your phone will work on, and more importantly what frequency's are available where your planning to go, because there are several bands around the world, and not all are in every country, so if your phone wont work on the frequency of where your gong, unlocking it is a moot point, because it simply will not work, not unless they have a frequency that your phone will work on, as I say there are a few, the US uses a lot of CDMA and TDMA, the rest of the world mainly uses GSM, and even GSM has a few variations, eg 900, 950, 1800 etc, so we need to check this out before anything else.

Now not knowing your phone I've had to search for it's frequency range, but you will need to confirm this as I may of got a different model to yours (I saw a couple of variations), anyway this appears to be what your phone will work on:-

If this is correct you should be OK, but let me know where your going, and confirm if these are correct, then I can tell you for sure if it will work there.

That seems to be correct. As for my destination, it is Caracas, Venezuela.

Thank you very, very much for your prompt and thorough reply; it was really helpful!

Right then, from what I can see your phone "should" work there, BUT, it is extremely limited in frequency choice, and that could mean many areas where you wont be able to get service, the fact your going to a major area suggests you should be fine and have no problems, but if you aim to venture out and about you could find service a problem.
Now there appear to be 2 networks to choose from there, they have a 3rd showing, but it's not up and running yet from what I can see, but here are the details of what they have, hopefully you will be able to find the better one for you.

Corporacion Digitel C.A. (DIGITEL GSM)
Operator Name: Corporacion Digitel C.A.
Network Name: DIGITEL GSM
Technology: GSM 900
Network Status: Live September 1999
Web Site: www.digitel.com.ve
Coverage Map
Roaming Partners
United States:-
AT&T Mobility; 3G 850/1900
AT&T Mobility; GSM 850
T-Mobile USA, Inc; GSM 1900
AT&T Mobility; GSM 1900

Telcel C.A. (Movistar)
Operator Name: Telcel C.A.
Network Name: Movistar
Technology: GSM 850
Network Status: Live December 2006
Web Site: www.movistar.com.ve
Coverage Map; There isn't one, but you may find more info on they're web site, but this usually suggests coverage is so poor they don't want to show how bad it is, so the other one looks the better choice ATM.
Roaming Partners
None that are listed, but it doesn't mean they may not of changed this since the info was last updated.

The other one is called Telecomunicaciones Movilnet C.A., but I do not know what it's status is, the date given (estimated) for the launch was May 2008, so the info is pretty dated now, so may not be as accurate as it should be, but it was said to be using the GSM 850 band