Shoe-mounted flashes:
I only know a few photographers who keep their flashes in their hot shoe--but the flash head is pointed straight up, and they always have a white sheet of paper with them so they can handhold the paper as a bounce reflector (they never point their flash directly at their subjects).
Flash brackets:
Although many photojournalists I see do use their hot shoe for their flash, just about every other photographer I know uses a flash bracket. Many use the simple bar-type. Others use articulating Stroboframe brackets (to accommodate verticals). It's interesting how they set-up their brackets--they all set-up their brackets so that the flash head is as close to their lens height as possible, and as near to the lens as possible (see below). Some have custom brackets. Some home-bent ones. Some have really cool factory-bent ones.

Flash bracket-mounted Speedlight.
I have both a plain, straight bracket, and a Stroboframe VH2000, which I used to use whenever I used my flash. When I did use it, my SC-29 would sit on my hot shoe, and my SB-800 would go on the bracket.

Generic-brand straight flash bracket ($8.00)

Stroboframe VH2000 rotating flash bracket ($59)
This particular Stroboframe bracket sets the Speedlight fairly high above your lens. This is good if you want to attach a Westcott, or similar, softbox to your Speedlight head. But most event photographers I know use brackets which put the flash head much closer to their lens. Ideally, if I were to use a flash pointed directly at my subjects, I would mount the unit upside-down, and mount it so that the flash head is just above the front lens shade.
The Clip:
But, now whenever I use a flash, I always handhold the flash, and bounce it off a white vertical wall using my SC-29 (I never put my SB-800 in the camera's hot shoe). If I know I won't have white walls, I'll slap my Lumiquest or Westcott softbox onto my SB-800, but still handhold it, off-camera, with its SC-29 cable still attached. I basically have completely moved away from a camera- or bracket-mounted flash set-up.
Since now my flash isn't mounted on a bracket, or the camera, I needed a place to hold the flash when I wasn't using it. So I put one of those super-sticky cell phone hooks on the side of my SB-800 (below), and I carry it hooked onto my right-front pants pocket. I wear my Quantum Turbo battery on my left hip. Works like a charm!

The Clip.
Are there any other clever off-camera flash solutions anyone else here has used? Either off-the-shelf, improvised, or innovated? Any cool flash brackets you found and liked? Show us your brackets!