Since we're on the countdown to the World Fantasy Convention (with its dual themes of urban and gothic fantasy) and since Flow has now been out for six months, I'd like to talk a little bit about what makes a setting work for me in contemporary fantasy. (I do consider Flow contemporary fantasy rather than urban fantasy. I'm aware this is largely a matter of nomenclature, but I have specific reasons for it - more in another post, probably.)
For me, the best reason to use our modern-day world in a story is the wealth of background available in the history - and the present! - of the occult, mythology and religion. Strong contemporary fantasy takes these elements and builds the backdrop from them ... or if it starts from another concept, incorporates them in the development. To me, to simply slap some magic invented wholecloth onto a private detective or ballet dancer or accountant misses the point.
As in any other fantasy, the magical element needs to be an integral part of the setting; it needs to feel organic to the history and beliefs of the people practicing it. If the magic is divorced from the rest of the world, it becomes unconvincing. Now, I've focused on real world "magic" here because it seems the most obvious and easiest source, and to me it's also the richest, but it's not the only option: it's also possible to build modern-day supernatural on scientific concepts. (It's why I was so fascinated by Rachel Caine's Ill Wind and her very climatically sound weather wardens, though I was less interested in the other concepts she introduced. Those felt less organic, to me.)
Another nice benefit is that a reference to history makes the magic feel suddenly authentic. I handle the arcane elements of an online roleplaying game where the Great Depression was the creation of a group of dark mages intent on feeding off the despair and emotional pain of the victims. History often seems so random - providing an occult explanation can be very satisfying.
On the other hand, contemporary fantasy doesn't need to select a mythological beast, divination method, historical legend and use it one hundred percent by the book. A twist, interpretation change or new direction can give a writer new options ... and offer a pleasant surprise for those readers versed in the base mythos. Of course, these changes can't throw the baby out with the bathwater - there had better be an explanation for why the bulk of folklore says something different.
So that's my take on the best way to incorporate the supernatural in a modern setting.