As of the start of Fallout 4, it is the 210th anniversary of the Great War and the bombs dropping, at October 23rd, 2287. It's also the same day the Boston Red Sox won the World Series in Fallout. They broke a ridiculously long losing streak that day. And ended the world at the same time.

Fallout (2161) Fallout Tactics (2197-2198) Fallout 2 (2241) Fallout 3 (2277) Falout New Vegas (2281) Fallout 4 (2287) There's a lot to sift though, but here's the [url=http://fallout.wikia.com/wiki/Timeline]Fallout Timeline[/url]

Depends on what game your playing but as of Fallout 4 2287.

According to wiki; the year is 2287

2290's ish