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.
The controversial Tome of Battle was revamped in Path of War. Notably, while the system is a Pathfinder version of Tome of Battle's, none of the Tome of Battle classes or disciplines have counterparts, so as to avoid rights issues.
Magic of Incarnum's meldshaping was reworked into the veilweaving of Akashic Mysteries. Like Path of War, it avoids having direct counterparts to its predecessor's classes. Unlike Path of War, the fluff around Akasha is considerably different to that of incarnum.
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.
The Warhammer 40,000Gaiden GameNecromunda is a heavily streamlined version of the early 90s game Confrontation with fleshed out background. Serialised in White Dwarf, Confrontation dealt with running underhive gangs in small scale skirmishes and what went on in the downtime between them. The game was known to be exceedingly complex and terrifyingly lethal (roll up a gang in a few hours, have the first guy killed within a minute of starting to play) but interesting nonetheless.