Best game? Or favorite game?
If you literally mean the "best", then there'd only be a very small list. Depending on criteria. Things like best selling, most influential (genre defining/standard setting), things of this nature.
However, if you mean our favorite, then you're going to get a lot of different answers.
As for me, I'm torn. Part of me wants to pick Homeworld as my favorite. Another wants to pick Banjo-Kazooie. Yet another wants to pick Half-Life 2 and it's Episodes. Still another wants to pick Portal, Portal 2, Sins of a Solar Empire, Starcraft2, and a host of other titles.
However, I think I'm going to have to go with Half-Life 2. (probably not surprising to a few people who know me) It not only redefined a genre but set standards that are still in force today. Has it aged? Of course. Has it aged well? In some regards yes. In just as many, no. Is it a game everyone can love? Obviously not. But it's hard to say it wasn't one of the most influential and most finely crafted games in the history of the industry without coming off as disingenuous. Regardless of whether you liked it or not.