I would say, as an heavy boost user, that today boost is no longer required. Most of boost basic utilities have either been incorporated in or superceded by the standard library.
Boost is still very useful for many advanced or domain specific libraries.
There are still a lot of minor conveniences, like lexical_cast, or uuid, or various helper algorithms (esp. for strings), that aren't subsumed, or at least not fully.
Also, one big deal is Asio. Which, granted, can be had separately from Boost... but Boost offers a convenient place to get it along with other minor stuff.
Then there's the question of how up-to-date the C++ implementation you're coding against is. A lot of stuff is nominally in the standard library, and if you use the latest and greatest, you might even have it out of the box... but for many people, they're still working on, at most, C++11 compilers, and so they need an outside source for stuff like filesystem.
Boost is still very useful for many advanced or domain specific libraries.