Back in the earliest days of gaming, the only reason a game would come to an end was due to the limitations of computing. Games like Pac-Man aren't meant to have an end, but once you reach the limits of the RAM at level #256, you get to a kill-screen. That being said, the programmers intended it and many other arcade games of the day to continue until the challenge forced players to die and pump in quarter after quarter until all allowances were spent!
These days, an endless game could be anything from a sandbox or open world, neverending, game like Minecraft to a game with a nonlinear ending such as Grand Theft Auto V that allows players to continue playing - or avoid "beating" the game for as long as they like. As these games are rising in popularity, more and more open world/sandbox games are being developed where the people coding the games have no intention of ever allowing a player to reach the ends of their games... mostly because one was never programmed. While some of these games might have a theoretical story ending, players don't have to meet them if they don't want to.
The best games without an ending can lead a player down a rabbit hole that keeps them playing games forever, but not all endless games are created equal. Of the thousands of video games out there, these endless games are the best of them all! Vote up the games you love to play forever.