There are a few ways to handle it that Ive seen.
Willful ignorance like in the Dresden Files - This is particularly aided by the antagonism of magic to Technology, which gives a believable mechanism for modern recording tech's not catching wind. Others like Supernatural (tv show) just kind of assume that nobody wants to be called Crazy along with lots of denial.
Active Conspiracy - pretty self-explanatory, either mortal or immortal agents.
Active Spell/mystical cover-up - The Percy Jackson books took a pretty direct version of this route: The Mist, which is a naturally occuring energy field (for lack of a better word) that completely hides supernatural events in the minds of the muggles present, replacing their perceptions with something more believable in real-time. This was particularly interesting to me because while nearly everything had some kind of supernatural Power, they defined actual Magic as the ability to manipulate the Mist itself. Also interesting is that while the other supernatural elements are pantheon/mythology specific (Greek/roman, Egyptian, and Norse all have series in the same world) the Mist is more universal. It was a fun trope.
Recent Development - Some event or change or cyclic resurgence that explains why the supernatural doesnt have a presence in accepted History but is around now. Limits the sort of entrenched society you can have, to some extent. One setting had the proto-dieties (Titans/Giants) having recently broken free of their ancient prison, which stirred up all sort of things, as an example.
Population growth - this is one that Ive sen mentioned but cant site an example work off-hand. Its a corollary to the Recent Development bit, which hinges on the idea that magic only manifests rarely in a given human generation, but with the "recent" population explosion what used to be a "once in a generation" sort of occurrence is now far more common by simple math. This requires a more Human-centric magic setting, though.
