For people who require a visa prior to arriving in South Africa, a disclosure must be made on the application form.
For people who can obtain a visa upon arrival in South Africa, criminal history does not form part of the landing interview, so if it does not flag up when they scan your passport then you're good to go... with some reservations...
If something happens while you are inland which prompts them to investigate you further, and they learn of a prior conviction that you did not disclose, you could be facing detention and a removal order. Based upon what you wrote in comments for example, it's likely that you have already been an illegal entrant in the UK because you did not disclose a material fact at the border even though it was not asked (deception by silence, Immigration Act 1999)
Another important consideration is whether or not you are entitled to deny a criminal history. And the answer to that will depend upon two things...
- What you were convicted for; and
- What, if any custodial sentence resulted.
South Africa, like much of the Commonwealth, has a law Criminal Procedure Amendment Act 65 of 2008 which lists the number of years that must elapse before you can deny a conviction. It's a complex area of law, and your question does not provide enough detail for amateurs to make an assessment. Most convictions will roll off after either 5 or 10 years, but some convictions, especially those involving child sex will never roll off.
In some cases you are entitled to deny a prior conviction for everything except immigration, but in most cases your entitlement includes everything except government job applications. Trying to get an accurate reading from amateurs on the net is risky because the rules are different with each country and generally opaque to those not versed in criminal law.
Note that the link in the preceding paragraph is merely an amendment to a larger act thus even if you were to edit your question to include all the relevant information it would not take the place of a qualified professional with a history of dealing in these matters. So if you are unsure about the level of candour you should use at your landing interview in South Africa, it's emphatically recommended to arrange an email or Skype consultation with a member of the Law Society of South Africa.
Adding: Anecdote, I once had a client who did nothing more than be at the scene of crime and the area was closed off and everyone had to wait until the police arrived. She was interviewed by the police for a witness statement. When they got her witness statement, she was id'd, and when they ran it, the poor girl had a prior conviction in the US. Bad news for her. Classic textbook case of wrong time/wrong place...