Interesting topic! Thanks for posting. I've enjoyed seeing everyone else's replies.
Here's what I've going on.

Usually play on Continents or Pangaea map, standard number of civs, standard number of city-states, with all victory conditions on. I don't set any other rules on or off in the options.
Early Game: I grab a monument first so that I'm able to crawl my borders out a little faster to luxury resources and desired tiles. After the monument comes a scout who then goes out looking for ancient ruins and revealing the map so I can get the lay of the land. While that's going on, a warrior is grabbing a worker from a nearby city-state. Back at my capitol I'm working on either a shrine or a granary. I tend to take Liberty first, which is a strange choice given that I prefer to run tall empires. But, I find that the worker and settler gained by filling out the requisite policies allow me to lock down the land I want earlier. In other words, I like my area of control to be a known quantity as soon as possible so that I'm able to focus on population increase and improving my gold and science yields sooner than I would otherwise be able to. In the early game, I generally like to let the lay of the land and location of resources determine where I put cities. I'm also rather reactionary in the early game. Instead of dictating the development of my strategy, oftentimes I'm reacting to perceived threats, requests from city-states, or various other diplomatic pressures (yes, war included).
Playstyle: As I stated above, I like to run tall empires and am reactionary in the early game; however, once I reach the Renaissance era, my focus on improving my gold and science yields begins to pay off. I usually out-tech everyone on the map at this point, and the strength of my economy allows me to leverage power where ever I need to, whether it be buying the friendship of city-states, buildings, a military, or paying an AI to go off and do some of my dirty work. It is at this point in the game where I come into my own and no longer am a reactionary force on the map. I begin to shape the globe how I want it to be. I am a peaceful player, but that doesn't mean I do not focus on military. If the transition from Civ IV BTS to Civ V taught me anything, it is the need to not neglect a military in Civ V. Again, beginning in the late Renaissance era, I initiate a large military build-up and maintain my position as the first or second most militarily powerful civilization on the map. I simply don't use it to conquer. It's a deterrent to the most wanton and warmongering civilizations on the map and it is a projection of power where and when I need it to be. A strong economy is what anchors my strategy. All else stems from it. If I don't have a strong economy, odds are I'm running a quietly mediocre civilization that isn't particularly good or bad at anything.
Preferred Civs Arabia, The Netherlands, China, Korea
Impact of BNW I'm actually looking very forward to this expansion because I think it plays to one of my strengths, i.e. the administration of a strong economy. The trade routes are something I'm looking very forward to playing around with, and based on the MadDjinn's recent video with footage of Portugal, a strong economy plays into your influence in the World Congress, which is another exciting inclusion that I'm very much looking forward to. I love playing a diplomatic game. The tourism/culture mechanics will take me some time to get used to. I don't see myself leveraging them in the same way I leverage my economy. But, we shall see. I do like the fact that it opens up different victory types in a way that make them more appealing than what's there now in G&K. Who knows, it could completely change how I play. We shall see.