I could list off every last game I've ever completed but let's look at some of the edited highlights in no particular order:
The Last Story, House of the Dead: Overkill, Neverwinter Nights, Dead Space: Extraction, Sonic R, Gun, Persona 3 Portable, Persona 4, Fire Emblem: Radiant Dawn, Tales of Symphonia, Resident Evil 4, Dead Rising: Chop til you drop, Urban Chaos: Riot Response, The Sky Crawlers: Innocent Aces, Ace Combat: The Belkan War, Super Mario Land, Castlevania: Portrait of Ruin, Tomb Raider (The new one), Sakura Wars: So Long My Love, Silent Hill: Shattered Memories.
There's quite a few there but hardly exhausting, and nobody finishes poker or football, really, because in all games, especially those involving multiple players, the game "ends" when one person/team has fulfilled the conditions for victory, many games nowerdays have decided to go the way of movies and TV and focus on narrative, in this case it is absolutely essential to have an ending, if you are campaigning for an end to narrative fiction for games then you are basically discounting all of Bioware's contributions to gaming, as well as works by Black Isle and Obsidian Entertainment which focus heavily on the story. Sure there is a place for both types of games, I mean Tetris turned the Gameboy into a hit sensation, with Nintendo still dominating the hand held market even today but story is important, and if people aren't reaching the endings of these stories then perhaps the devs should ask themselves why their game isn't engaging enough for people to want to play through to the end.
"There are many parts of my youth that I'm not proud of. There were loose threads - untidy parts of me that I would like to remove. But when I pulled on one of those threads, it unraveled the tapestry of my life."