UPDATE: I've since this was written replaced Boost.Log with my own custom logging, mostly because I decided to get rid of all Boost dependencies in all my projects for various reasons. If you are fine with using Boost I guess Boost.Log is still a valid choice judging by Klaim's answer.
My experience with Boost.Log in year 2010 follows.
I've successfully integrated Boost.Log in my game engine and I can only talk good things about it. Sure, it's a little early to use, since version 2 will be the actual version that will become the official Boost.Log.
Beware that the version "1.0" available is not being maintained. To receive updates you must use the bleeding edge (trunk) version which might become unstable. Take this into account if you are going to use this version in any serious projects. If you are not afraid to use bleeding edge versions or future breakage, then go for it. It's really nice to use as it is in its current state.
I've long thought the hierarchical logging system in log4j/log4cxx was superior, but Boost.Log has got me thinking otherwise. Filtering and attributes is way more flexible.
The design of sinks separated by frontend/backend makes it really easy to add additional backends. No need to worry about synchronization issues or filtering which is handled by the frontend.
The library also comes with lots of backends already, rotational files, console, syslog, Windows event register, etc.
I have written my own sink backends; one goes to the in-game console and one to a kind of notification system for more serious events. Was easier than I expected, had it up and running in just a few minutes.
Last but not least, the maintainer/developer is really helpful as well. You'll get plenty of help in the project forums. He's fixed two bugs (whereof one major) just this weekend that I reported :-)
boost::log
is slow. – Lease