My classic list would be:
Portal: Has all the elements of a classic, unique gameplay, memorable characters (despite the fact you spend most of you time alone), and an credits song that could be considered a cult classic by-itself.
Bioshock: While regarded as System Shock Under the Sea, the characters, world-building, and infamous plot twist plying into gaming tropes will ensure it will be remembered for years.
Call of Duty 4: The game that started the MMS craze was rather good, nice pacing, interesting locals, and kicked off the 'shock scene' phenomenon. Pity the sequels have forgotten most of what made the original campaign great.
Minecraft: A sandbox without compare, this one will will last the ages.
Bethesda Open Worlds: Oblivion, Fallout 3, Skyrim. Those are the titles other open world games aspire to.
Batman: Arkham Asylum: Before AA, most tie in games like this were regarded as crap. After AA they are still regarded as crap but now people ask "is it as good as Arkham Asylum?"
The Cult Classics are a little different, they are the ones that will be remembered not by the whole due to certain factors but nonetheless will remain in the minds of many.
Spec Ops: The Line: The Line was a product of its time, when MMS were going beyond over-saturation and ridiculousness. The Line took the gameplay and story tropes of that genre and turned them on their heads, showing us how twisted it was and that we should be ashamed for enjoying them.
Dark Souls: Some may wonder why its in the Cult Classic pile, but hear me out. In a time of 'broadening appeal' and to be frank dumbing down of mainstream gaming Dark Souls was a welcome change. Its punishing difficulty will keep it in a niche (and hence keep it in this category) but that isn't bad. I wish there were more games like it.
Fallout: New Vegas: This game can easily slip into the Bethesda category but also has a place here, mainly due to Obsidian and the original Fallout creators bringing us a continuation of the fist two games.
Saints Row 2: The game that stepped out of GTA's shadow and became its own.