Yep. I always hated even the idea of it. But I started running this past January. I am 43. I love it now. Not the heat/humidity so much the past 2 months, but the actual running? LOVE. IT.
Can't say why or how. Just start very slowly and don't force it. Walk a minute, run 15 seconds. Walk a minute run 15 seconds, etc... for a mile, on your first time out. GO very slowly. Seriously, as in please follow the "talk while you are running, if you can't you are going too fast" rule. You will build speed/ distance over a few weeks and you WILL be able to run a mile, and then some.
What made me change? Hmmm can't really say. Perhaps injuring my knee in December, and realizing upon recovery that I might not be ABLE to for physical reasons if I don't start now.
ETA: Go online to Runner's World and read some of the articles/items there. LOTS of people take up running at "later" ages. If you start slow and don't push too hard, you can avoid injury. And be aware that your breathing will be the thing you are most aware of at first. I didn't use music for the first 2-3 months. By then, I worked up enough distance that I was getting bored without it. And go outside to run, if you can.
Sorry, had to ETA2: Find a nice place to run (jog/walk) outside... and use the odometer on your car to check distance. It was one of the most motivating things for me. After I'd run, I'd get in the car and go drive it and see exactly how far I went. It's very inspiring to suddenly one day go an extra quarter mile. And then, one day you just keep going... and do 3 miles. And then you start wanting to really challenge yourself and start adding extra turn outs or side routes... and it is fun trying to estimate in your head how much extra distance you are adding in, and then driving it afterwards to see.
I always feel yuck the first half mile.. but usually about 3/4 into the first mile things start clicking and I enjoy the rest of it. And feel fantastic after. I actually get crabby and easily aggravated these days if I don't get a planned run in.
Feel free to PM if you need some more personalized motivation or ideas. :)