There is a convenient Library of Congress article that details instances across the globe where a supermajority is needed for certain parliamentary procedures, of which a filibuster is an example. There's a PDF in the link that contains the full report, including full references. Some examples taken from the summary, with the last two basically being filibuster rules:
In the Hungarian Parliament, a supermajority (four-fifths of the Parliament’s members that are present) is required to derogate from any established procedural provision and proceed in a way not prescribed by the Parliamentary Rules of Procedure to resolve a specific issue. Voting by two-thirds of the members of Parliament present is required to start debates on an urgent matter. Changes to the committee meeting agenda require a vote by two-thirds of the committee members present.
In Kosovo, a supermajority (two-thirds of the members of Parliament present) is required to deviate from the Rules of Procedure, and a qualified majority vote (two-thirds of all members of Parliament) is required for amending the Rules of Procedure.
If an opposition political group insists on continuing debate, discussions can be stopped if two-thirds of the members of the Seimas (the Lithuanian Parliament) participate in the sitting vote to terminate the debate.
Speaking time for a National Assembly (NA) member is determined by the Speaker and is generally up to fifteen minutes. However, when an NA member submits to the Speaker a letter of request of debate on an agenda without a time limit (filibuster) and with the signatures of one-third or more incumbent NA members, the Speaker must implement the filibuster. Then, an NA member may submit to the Speaker a motion for termination of the filibuster signed by at least one-third of all incumbent NA members. The motion is decided, without debate, by a secret vote twenty-four hours after the submission of the motion. The affirmative votes of at least three-fifths of all incumbent NA members are required for termination of the filibuster.
The South Korea example is pretty much exactly the same as the filibuster in the US Senate, with mostly cosmetic differences. It exists by an act of the NA, and not by constitutional requirement.
There are also often supermajorities mandated by constitutions.
A few select entries from that article:
In Canada, most constitutional amendments can be passed only if identical resolutions are adopted by the House of Commons, the Senate and two thirds or more of the provincial legislative assemblies representing at least 50 percent of the national population.
Article 20 of the Constitution of Denmark states that if the government or parliament wants to cede parts of national sovereignty to an international body such as the European Union or the United Nations, it has to get a five sixths majority in the Folketing (150 out of 179 seats). If the government or parliament are only able to get a simple majority, they have to hold a referendum on the question.
And the UK either has one constitutional requirement, or one voluntary requirement, depending on what the "constitution" of the UK really is (it strikes me as a voluntary thing, as the Parliament could surely amend or repeal it at any time, but I'm not familiar with the particulars):
The House of Commons (UK) can be dissolved and an election held before the expiry of its 5-year term by a vote of two-thirds of the membership of the House of Commons since 2011.