(Edit: My wife and I tried the SMS Roamer I mention in the post below. To my embarrassment, it didn’t work. Just leave your SA phone at home and pick one up here. Saves lugging unnecessary stuff all the way here.)
The bad news is that South Korea uses a different cellphone technology (CDMA) to SA (GSM), so your SA phone can’t be used there. Big bummer for me, because I have two perfectly good cellphones that I now have to leave at home and go buy some dodgy second hand phone when I arrive in Korea. I’m not looking forward to that.
But there is some good news. If you are a Vodacom customer you can arrange to use SMS Roamer. Using this you can take your SA cellphone to Korea, but all voice calls (incoming and outgoing) are disabled, and you can only use SMSs and voicemail. The SMSs from Korea to SA cost R2.50 each, and from SA to Korea R1.74. People can still phone you, but they will be diverted to voicemail, which you can access in Korea.
This seems like a good idea to me for the first week or so before we get organised with a local cellphone, especially as my wife is stuck with a Vodacom Top-Up contract until July. At least we can get some use out of all that airtime!