If only more studios knew what "game play" is.
This brings me to what my greatest games of all time are. This video (Warning: For reasons unknown to me there"s an excessive amount of not-safe-for-work language in this video, so, you know, don"t watch it at work or around folks who"d find it offensive) sums up the whys and hows better than I can. I"d recommend it as mandatory viewing for anyone involved with creating video games – it"s just unfortunate that the language precludes it from being used as a teaching resource for young"uns.
Anyway, whilst I do think that there are particular defining games that can easily be pointed out, I don"t think that there can be one single catch-all "greatest" game, since it"s such a subjective thing.
With that in mind, my top game of all time is Rockman & Forte for the Super Famicom (1998), which was later released in English as Mega Man & Bass for the Game Boy Advance (2003). The video above explains why so many of the Mega Man games are so well-designed, and that also applies to this particular game as well. Doubly-so in some aspects, because the two protagonists have different abilities, yet play through the same levels, and the game subtly "teaches" you how to handle both in the very first level.
My other top titles – since I really can"t pick just one, either, like so many others here – also include, in no particular order;
Mega Man 7 (SNES, 1995)
Mega Man X (SNES, 1993)
Mega Man Zero 2 (Game Boy Advance, 2003)
Star Fox/Starwing (SNES, 1993)
Mario Kart 7 (Nintendo 3DS, 2011)
Lemmings (Too many to list, 1991 to 1994 – My favourite is the Master System version)
Animal Crossing: Wild World (Nintendo DS, 2005)
Klonoa – Door To Phantomile (PSX, 1998)
Croc: Legend of the Gobbos (PSX, 1997)
Mappy (Arcade, 1983)
Donkey Kong Country 2: Diddy"s Kong Quest (SNES, 1995)
Scooby-Doo & Scrappy-Doo (C64, 1991)
Pulseman (Mega Drive, 1994)
High Seas Havoc (Mega Drive, 1993)
Mega Man ZX Advent (Nintendo DS, 2007)
Ms. Pac-Man (Arcade, 1981)
As you can see, I"m a bit of platforming nut (with a definite taste for arcade-style things), and definitely a Mega Man nut. Funnily enough, almost all of the games in the list mostly adhere to the crafting that's covered in the video at the start of the post.
If only there was room to write in my top 100! (I did that as a writing exercise a while ago, and it was more challenging than you'd think.)