How do you get invited to speak at high profile events?
My answer to How do you get invited to speak at high profile events? on Quora
SXSW has an open call for proposals—you’ll need to submit a suggestion to the panel picker and encourage people to vote for you.
TEDx events are run by volunteer teams—if you want to speak, get in touch with them as soon as you hear about the event.
There are plenty of conferences that only invite speakers—the trick to speaking at those is to give great talks at other events, build a reputation as a good speaker and then get introduced to the organisers (or introduce yourself).
We have a list if events with open calls for proposals here: http://lanyrd.com/calls/