I googled it - here are two different theories. I had heard the one about taking the deep final bow, but not the other about John Wilkes Booth.

http://www.theatrecrafts.com/glossary/pages/morebreakaleg.ht ml

I had a cast member actually fall and break a leg at dress rehearsal in a show I directed.  So, the phrase brings a whole new meaning of flashing lights and sirens!  It was a child, and we couldn't get ahold of his parents right away, so we had some not so pleasant moments figureing out what to do, with the poor kids screaming in pain. Now when I direct kid's shows, I insist on at least one parent, or guardian, being present at all times.

The most plausible one of ?break a leg? to me is #3 on the Suezysue site posted.
That being paid if the performer breaks the visual plane of the masking Leg drops.
When growing up, which I?m still yet to achieve in theatre.
I know from those who worked the Variety Halls, as what others  might call vaudeville, which my family was involved in long before I popped out at the stage door.
Nearly all the performers only actually were paid upon appearance on stage.
It would have came into vogue & in our case derived from the Music Halls, without the Chairman who compared & conduced the audience & the running of the shows performances & controlling the performers within the company, from the house. Where by Variety came about, from a lot of individual acts, thrown together at each performance. Theatre managers would accept & try out any acts which they thought would work & give the hook to those the punters rejected, signalled by the volume & quality of gears or fruit & vegies thrown.
At most variety shows there was always more acts than needed, to fill the bill. So what was considered the fairest way to pay, from the management point of view, was if a performer or act was to break the plane of the Legs & get an appearance. Even if the got the hook after getting on stage, they could demand appearance money.
Listening to the old troupers & stagers, there was a wide divide between variety halls & the film industry or what they considered legitimate theatre. Which was quite wide as most in Variety considered, getting a part in a play was the ultimate. Those who were in drama theatre, were adamant those who acted in films had sold their theatrical souls.
This would have been around the 20?s when actors  started to adopt ?Break a leg? from the Halls into theatre jargon.
As for it being used by old Bill as a stage direction in his scripts, as most of the writings, scripts & serving documents tend to prove. They were written by scribes, paid a few coppers to write out scripts dictated or as viewed. Because of the varied hand writing, spelling & styles within the same script.
So to break the leg, could be just down to the interpretation of the various scribes.
As for the others, why not add your own meaning to the collection of theatre superstitions & myths.      

 Thanks RD I have started to write a book of sorts, about growing up in theatre.
Well I keep kidding myself to complete it.
Your post has gone a long way to prompt me to get off my bronze & do it.
I attempted to write one years ago on stagecraft, at the advent of the PC becoming available.
I tapped it out & saved it on the old floppy disks, even fronted up a publisher, as I was rather chuffed with my effort. Only to be advised, if I crossed their palm with $10 000[AUD] they would publish the book. Which was in 3 main parts, ?Behind the pro?, ?Before the pro? & beyond the Pro?.  
The reason they gave for needing the gold bricks, was as it?s a stagecraft book, that would appeal to only the amateur theatre. The likely sales would be limited & restricted to the odd local library at best. Thus I would have to pay thru the nose for the print run.
What a laugh!
With the box of floppy disks, I drove to the nearest road side bin & chucked the lot in. Leaving them for the Garbo?s to utilise as land fill.
I wished I had of kept them especially now with DIY publishing & the net making it easier.
Also having since had a quadruple cabbage job & a few strokes, caused by extensive plumbing work.
Which has made it a bit more difficult, as I think I must of lost a number of cells.  Which probably rolled out on to the ambulance floor & have not been found as yet.
So I think at times I should scribble together a new book, while I?m waiting for them to be returned as lost property.
So I was thinking doing one under the title of ?The Naked Chook Pen? . But rather than hanging by the thumbs, waiting for it to happen.
Your idea might be a better option Red, except the topics I have started on forums in the past, have lasted about as long as an outside Dunny in a cyclone!
Honestly I think there is others here that would have had a more fasinating & colourful grounding in theatre than me.

 You know how to over inflate a flattered ego, Cast me!
Really it took me about the first 5 years of my life, to truly realise that other folk didn?t live the theatre life as well.
As my great uncle Joe owned an Opera house & theatre in the city, & he managed to have a minument built to him near the theatre in Westgate Road, Newcastle upon Tyne UK.
Also even watching performers on the screen at a near by picture house, it took me a while to connect were not all born the game. I must of lived a sheltered youth or as completely dense as short planks, while growing up on the theatre circuits. That in fact all those I called aunty or uncle, were in fact not related to me.
To me it was not particularly seem exciting or fascinating, by the time I became 6 going on for 30, as I didn?t know there was anything better or more normal anyway!
The only significant thing I do remember was a very long lay off, when I was about 8 or 9 & we returned to our home in Tyneside. My dad went back to work in his profession, with Rolls Royce. He would come home every 5 weeks or so, & spend a week. He was always dropped off or picked up in Roller, because he preferred not to drive. Although he always reckoned it was because of his dodgy knee & finally gave up the stage all together. When he had to  have a couple of operations on his knees & hips.
Although all our neighbours used to think we had plenty of the readies, seeing the Rolls Royce parked out side ocationally.
The rest of the family carried on for a while & he would link up in various towns.   But it was the beginning of the end for the variety circuits, when TV came in to vogue. So mum retired to do legitimate plays in theatre & my sister went on as a dancer with the Val parnell Empire Theatres. I was packed off to a rather toffee nosed private school, which lasted a very short while. Primarly because I became the butt of the more couth of the other students & prefects. Which lead to me given them a few bloody noses in retaliation & I refused to be a servant on call to the senior students.
Prompting them to seek me being sent down & all that terribly British school discipline, That I pulled the pin one day & headed for home. Arriving almost after midnight, to be greeted by my very surprised & concerned mum. 
So I just settled down & then came out to Australia on my own at 14.
So that?s virtually it all neatly wrapped up & it is about as fascinating as  the average contents of a plastic lunch box.