I am referring to paragliding - see http://en.wikipedia.org/wiki/Paragliding. If I have a preference, I prefer to watch paragliding to hang gliding - see http://en.wikipedia.org/wiki/Hang_gliding. I suppose it must be the slower, more graceful, and photographically more interesting way that paragliders move through the air.
You don't seem to see so much hang gliding done nowadays. That may be due to the less expensive and much lighter equipment needed for paragliding - basically an aerodynamic fabric wing held into shape by cords, with of course a harness, almost always attached to some kind of 'seat'. The key parts of the ensemble can be collapsed into a backpack. Whereas the rigid struts needed for a hang glider mean more bulk and weight, and setup is more of a rigmarole.
Another point would be that hang gliders fly horizontally, face down, and landing safely is trickier. Paragliders can land on their feet. But of course both variations are at the mercy of the wind, and a sudden gust, or an unexpected drop in the wind, can be potentially hazardous. A hang glider, with a wing that can't deform, is more suitable for very strong winds, and can fly higher. All such considerations are irrelevant to me, because there is no chance whatever that I will ever let myself get airbourne by either method. But I like to see others do it, and I admire their skill and fearlessness.
Over the years, I've amassed quite a collection of paragliding shots in various locations, usually taken close to sunset, when the image of the solo high flyer drifting into the setting sun is at its most potent. Here's a selection (from 2002 to 2013) taken from the South Downs and Beachy Head in Sussex, and at Rhosili on the Gower in South Wales:
What a sense of freedom these shots give me.