This is currently my favorite method of solving. I solve two opposite faces, then a U-shaped area around each of them, then two more adjacent faces and the edge between them, then the last four corners and the remaining edges.
Note that this video is sped up at 2x speed because I can't solve the cube faster than KZread's 10-minute restriction :)
Better-quality videos (without the speedup) are at www.weihwa.com/~whuang/videos/...