Pathfinder is Paizo's refinement of Dungeons & Dragons 3.5 edition rules, made after Wizards of the Coast released 4.0 edition and upset a lot of fans because it was completely incompatible with 3.5 and was a sharp change in play-style.
Dreamscarred Press has made a habit of taking Dungeons & Dragons's alternate magic systems and porting them to Pathfinder.
Psionics were revamped in their Ultimate Psionics book, with significant chunks being outright conversions (due to the rights situations, for the other systems Dreamscarred had to keep to making sequels to the systems while avoiding looking as if any specific content in the originals got a successor).
The controversial Tome of Battle was revamped in Path of War
Magic of Incarnum's chakra was reworked in Akashic Mysteries
The OGL fostered many of these for Advanced Dungeons and Dragons First Edition: Among them are Castles and Crusades, OSRIC, and Labyrinth Lord.
Cheapass' Games Kill Doctor Lucky is a spiritual prequel to Clue.
Magic: The Gathering Arena of the Planeswalkers is the successor to Heroscape as it is made by the same designers and basically just takes Heroscape and puts it in the Magic: The Gathering universe and adds magic cards but is 90% the same game. It even has compatable terrain and some even say armies and almost everyone that has both games has tried mixing them.
Hordes/Warmachine by Privateer Press is considers by many to be a better version of Warhammer Fantasy and 40,000, as many Games Workshop designers left to start Privateer Press for the purpose of not only making a better game but in their opinion a better game company.