Video games are no different than other any other form of entertainment.
Any product that earns substantial amounts of money will be milked as long as possible. Sometimes that results in games getting progressively better throughout the life of the series.
Other times, however, the sequels fail to measure up to the original.
Rarely do critically acclaimed or strong-selling games not receive the sequel treatment.
For one reason or another, these games never spawned a sequel and should be games you should track down if possible.
Mirrors Edge (2008): This EA release could very well still get a sequel. Its new enough, and there have been rumors of one. But in the age of quick greenlights for remakes, Mirrors Edge stands alone. The game pioneered a first-person action game (largely) without shooting. You play as a messenger who uses parkour and free running to navigate through the rooftops and buildings of a futuristic city.
Altered Beast (1988): While this game technically had a spin-off (although it was only on the Game Boy Advance), it has never really received a full-on sequel for a console. I -- and many others -- fell in love with this game at the arcade as a child. I remember playing it over and over when it came to home consoles on my cousins Sega. Altered Beast wasnt a revolutionary game, but instead just a fun beat em up that allowed the protagonist to morph into various half-man, half-animal creations.
Super Mario RPG: Legend of the Seven Stars (1996): Mario received his very own role-playing game in this game for the Super Nintendo. It doesnt offer the depth of modern RPGs, but Super Mario RPG is plenty of fun and is available for download on the Wiis Virtual Console.
Braid (2008): Old-school 2D platformers have experienced renewed popularity with vehicles like Xbox Live and the PlayStation Network to utilize for releasing games. Braid is the best so far. Protagonist Tim moves through stages with the ability to influence time to solve puzzles. It was the first truly great Xbox Live game, and it paved the way for future games like Limbo and Shadow Complex.
Ico (2001) and Shadow of the Colossus (2005): I grouped these two together because both were developed by Team Ico and both debuted to great reviews when they were released. But Ico didnt sell well at all, while Shadow of the Colossus sold moderately well. Both games are prime examples of a minimalist approach; the landscapes are bleak and empty. Both protagonists find themselves in an epic quest. Icos trying to rescue a girl from a castle and Wander hopes to resurrect a girl by slaying 16 giant colossi. The games are two of the best ever released for the PlayStation 2, and luckily enough, they are being re-released for the PlayStation 3 in 2011 as Ico and Shadow of the Colossus: The Collection.