I asked a Roman Catholic priest I know to give my household's old iPhones to the poor during his trip to India last year. I had originally planned to sell them when I had a chance after upgrading myself and my parents, but I changed my mind when I heard he was going to visit his village in India where there are many poor people.
You could ask your local Roman Catholic parish if any of the priests plan to travel to poor places. They tend to be from all over the world, many are from poor places and they tend to visit family every year or so. They would definitely be able to give your phones to the poor.
Just make sure that the phones are unlocked, supports GSM internationally (if it is a US phone) and have a charging cable. In my case, I neglected to realize that the NEMA outlets used in the US are not typically used in India and included the US chargers. Compatible AC to USB chargers are cheap enough that it was not a big deal.
Also, models like the Virgin Mobile iPhone 4S whose baseband is programmed to only connect to US CDMA networks would only be useful for parts in many other countries. Phones that are locked to CDMA in the US, but support GSM when unlocked for international use, like the Sprint iPhone 5 will work fine, provided that they are unlocked before they are sent.
If it is a CDMA only phone that is not locked to the US, you could check to see if the country where the priest is going has a network compatible with it, although it is hard to find coverage maps for CDMA outside the US to know if those networks would actually be relevant:
https://en.wikipedia.org/wiki/List_of_CDMA2000_networks http://www.memphissoftware.net/img/coverage1.jpg
There is no reason there shouldnt be a 3G, 4, 4S capable of owrking and in the hands of "the poor"
Why not a turn-in system where older yet still functioning phones are given to anyone who wants them.
I personally am guilty of not properly handling my old phones. I've had every single generation of the iPhone since the initial launch. I've broken 17 of them to date. I have no clue where the other 16 are now, aside from one.
I'd happily have contributed my old phones to some program where either poor or kids can have them freely.