The method of joining rope described by Alex and the variation shown in the picture is common in the rope access industry. Or at least training in the rope access industry. It wouldn't be considered good practice to have rope joining knots in an industrial environment due to the very complicated rescue issues that knots can cause.
Having said that I've just received a catalogue from a UK equipment manufacturer and the picture on the front cover is a window cleaner just abseiling down to a Double Fisherman's knot in one of his ropes on a very tall building in Asia. There would usually be a Fig 8 or Fig 9 loop knot to accompany it for clipping into as you pass the obstruction but not in this case. Another issue to consider, particularly on very tall buildings, is the amount of rope stretch there would be on the safety line in the event of a working line failure. If the building on the photograph is what I think it is then if there were a working line failure when the window cleaner was 25m from the floor, he would probably hit the floor. I digress...
In industry, one of the most common methods of isolating a damaged section of rope is with an Alpine Butterfly so it is technically possible to join 2 ropes with an Alpine Butterfly. You would treat the two ends as being the loop and then tie in the normal way. By normal I mean the way I normally teach it which is by taking a bight and putting two twists in it. Its not so easy if you use the mountaineering method of wrapping three loops around your hand. Like the stories in the report posted by AL, its unlikely people would be happy with joining ropes with just an Alpine Butterfly, the next step would be adding an Overhand knot behind the Alpine.
Getting back to 'Y' hangs.
As I said before, I think simple is usually best and being able to tie a Bunny knot, Alpine Butterfly, Fig 8 (including rethreading) and a Fig 9 will cover all the rigging you are ever likely to do. If, in addition to the above, you can tie a double or triple twisted Scaffold knot on the end of your Cow's tail you would pass the knot tying element of an IRATA Level 1 course. You would get a Exam Discrepancy if you tied a Cavers Butterfly instead of an Alpine and you couldn't rectify the mistake. The Alpine Butterfly is the only industry accepted Mid Rope knot with all the others (above) being End Of Rope knots.
I do like to see good rigging in caves. Most people first learn about rigging simply by following others and if others are rigging well then they will learn good rigging. If they follow poor rigging then they will learn poor rigging.
Good rigging for me is not just about appropriate knots for the situation, properly dressed and set (I am a bit of a stickler on that but not quite a nazi I hope), but its also about ensuring consideration has been given to people of all abilities and sizes negotiating the obstacles, particularly when they are returning up the ropes and having to get off at the top with heavy bags. We encountered that problem during many of the recent Berger trips.
Mark