I have a valid residency permit (till March 2017) for the Netherlands. I was wondering, would I be able to travel to the Czech republic with it, without having to apply for a Schengen visa? I am South African
According to Article 6, paragraph (1)(b) of the Schengen Borders Code, a residence permit issued by a Schengen member state exempts the bearer from any requirement to hold a visa:
1. For intended stays on the territory of the Member States of a duration of no more than 90 days in any 180-day period, which entails considering the 180-day period preceding each day of stay, the entry conditions for third-country nationals shall be the following: (b) they are in possession of a valid visa, if required pursuant to Council Regulation (EC) No 539/2001 (25), except where they hold a valid residence permit or a valid long-stay visa;
Both the Dutch IND and the Czech Ministry of Foreign Affairs agree your residence permit is indeed enough to travel in the Schengen area without a visa:
Persons belonging to one of the following categories may stay temporarily in the Czech Republic/Schengen area without a visa:
citizens of the EU, Iceland, Norway, Lichtenstein, and Switzerland – see chapter "Stay of citizens of the EU, Iceland, Norway, Liechtenstein and Switzerland in the Czech Republic";
citizens/holders of travel documents of a state, with which there exists visa-free regime
holders of long-term visa "D" issued by any Schengen state - this visa contains a function of a Schengen (short-term) visa;
holders of a long-term or permanent residence permit in another Schengen state and the stay in the Czech Republic does not exceed 90 days (3 months);
Travelling with your residence permit
With a valid residence permit and a valid travel document you can travel to and stay in the Schengen area without the need for a visa.
If your residence permit is expired or will expire during your trip you may apply for a return visa while awaiting the procedure to have your residence permit extended or changed.
Flights between the Netherlands and the Czech republic are effectively domestic, meaning no border controls. Literally as if, say, flying from Cape Town to Durban.
In addition, as pointed out by phoog, the Schengen Border code stipulates that holders of a residence permit in one Schengen country can visit the others for 90 days in a 180-day period.