Very few. It's not a question of permission. If you read (and nobody does) the contract of carriage for each airline, you will find that you have agreed to paying a fare for a ride from point A to point B on a particular day. Yes, we all choose which flight we want, and what seats we want (in most cases) but the airlines can change that flight at any time. The majority of airlines won't give you a refund, or allow you to make a free change, if the flight change was less than 3 hrs or so. With that in mind, they usually don't make changes of over 3 hrs. But...they can cancel your 7am flight and put you on an 8:15 flight, then a month later change that to a 10am flight. So....while it is 3 hrs difference from your original flight, it is not 3 hrs from the most recent flight.
I always book knowing full well that they can, and probably will, change my flights. I just book the one I prefer, at the fare I want and then hope for the best. So far, for my flights in August, the changes have all been in my favor. But, we still have 29 days to go and we're flying JB down and Delta home...lots of change opportunity there!!!
This is one reason I've started flying SW more often. I know that my flights will pretty much stay the same. Equipment issues can come up but that's understandable. Same thing with weather issues. But, they don't just willy-nilly make changes. That's one reason they hold back their booking window so much longer than other airlines. Yes, you have to wait longer to book, which makes some of us nudgy, but you'll be on the flight you booked.