A friend sent me a video about how bad too much sitting is (see some examples below), and my new experience confirmed this. Then I was told about a program that would interrupt you on the computer and force you to take regular breaks. One of these is Stretchly, and it works wonders!
It's free, open source software that works for Windows, Mac and Linux. Every now and then you are asked to take a "microbreak" of a few seconds, and there are helpful tips to suggest how to take the break. And then about every 30 minutes or so you should take a proper break from the computer. Get up and walk around, and give your back a chance to recover from all the unhealthy sitting (and slouching in my case).
To force you to take the break it puts a big box right in the middle of the screen. The microbreaks only last for a few seconds, but the full break is 5 minutes. Most chiropractors will tell you to take a break from sitting at least every 30 minutes, and Stretchly helps you do this. If you leave your desk for more than 5 minutes before the enforced break, it resets its timers for you. And once the enforced break is up, it sounds a helpful chime to tell you the time is up, so you don't waste time or have to stand around checking the screen.
Since we can only concentrate fully for up to 20 minutes at a time, these breaks actually make you more productive, because they help you regain focus and think about what you are doing. I was apprehensive about this at first, but I find my code is much less buggy and more well thought out because of the enforced breaks. There are plenty of useful features in the program, and if you are going to watch a movie or you need to connect to a client's computer for remote support, you can pause the program for a while. There are plenty of options you can tweak to get it to work just right for you. Check it out!
One final idea from the 4th video below: stand up every time you take a call or use your phone. Great idea. Put the phone somewhere other than your desk to make this happen. It will also reduce your exposure to the radiation from the phone. But that's another story for another day.
Update 19 May: Thanks to feedback from the developer, I discovered that you can change the messages that Stretchly displays, so I was able to add in the exercises that my Bio-Kineticist has recommended. I also found an Android app called "Big Ben Bonger" that plays the Big Ben chimes on my phone. I can set it to go off every half hour when I'm working on other people's computers.