Here's how I think about these things: The best is pretty much the same as my favorite. Since this stuff is all subjective, I don't think there exists a game that is actually "better" than all other games, if you catch my drift.
"The greatest" on the other hand I think is something that you can have an actual discussion on. The greatest, to me, means the most influential, the most important and frankly, it would also have to be immensely popular. For example, in popular music, the Beatles is the greatest band of all time, because it JUST IS. They were the most important in terms of influence of popular culture and other bands, they were the biggest phenomenon in the history of popular music by a huge margin (even Elvis couldn't touch the beatles in terms of popularity) and they wrote about 50 indisputable rock classics in a space of 10 years, and I don't mean they wrote some good songs. I mean they wrote 50 songs that no one can deny are absolute classics.
Greatest game ever? I couldn't even guess.
But all of that pointless ranting aside, the best game, or my favorite, would probably have to be Morrowind, Skyrim or Portal 2. There are plenty of games from the nineties like Ocarina of Time that I still think kick ass, but I can't deny that they have aged. Morrowind has aged as well, albeit not quite so badly. I liked Skyrim more in every quantifiable way, but I guess the reason why I still place morrowind so high on the list is because the atmosphere rules so goddamn hard.
As for Portal 2, I know I am in such a tiny minority in preferring it to the original but here is my explanation: I couldn't think of anything wrong with the first one, whereas the second one did have some flaws. However, the stuff that was great in the first one was even better in the second one, so for me, that is enough to tip the balance in favor of the second game. I just thought it was even funnier.