What year does Half-Life 2 take place in?
According to the wiki, it's set "Around 20 years after Half-Life 1"
According to the Half-Life 1 wiki, the setting of this game is set sometime in the 2000's.
It's listed on the wikia, actually. There are no specific years, but a range between the years of 2015 and 2029 is given near the bottom, as the first entry below that header is Gordon being awakened from stasis, which is the beginning of the game.