Programming is an artform. To know how to code is to be able to speak a language, in which you transform your ideas into reality. The joy when building your first application, and see it work, as you specifically told the machine it should, is simply amazing. Just as a kid learning to read stories for the first time.
Now, why should you learn to code?
To me, learning to code is at the same terms as learning math, to read, and to write. You do not need to become a "great" programmer, just as you do not need to become a professor in mathematics, or to become a great author to be able to use these tools efficiently to better your life. Just as learning the other basic skills, programming will create deeper understanding, and grow your possibilities exponentially!
Everybody should at least have an idea of how to program, and have some practical experience. Computers are replacing pretty much all the tedious manual work we, in the past, had to spent time and energy doing ourselves. This development will of course continue, and if you do not have any idea of how to program computers you will miss out on life, just as much as the people that haven't learned to read.
So how to learn?
This is the best part. As the internet has developed, there are so many amazing opportunities to learn programming completely free. You don't even have to install anything on your computer. There is basically no inertia to get started other than your own willpower! No matter what you do, you should be able to sit down 20 minutes every day and learn a bit of programming.
Here's some options (both free, and premium):
http://www.codecademy.com/ (free)
http://www.learnpython.org/ (free)
http://teamtreehouse.com/
(free and premium)
http://www.starterleague.com/ (premium)
There are many more options, go find them yourselves! Don't limit yourself to this selection.
Final words
Personally I love that I am able to build most of my dreams right away. However also programming can become tedious work, just as much as writing, and doing math. This is where the programming techniques come into the picture, and you are centralizing work, making it more enjoyable and faster to program. You will figure this out yourself on the journey!
Also I would like to say that you can perfectly continue your life without coding! But what I say is that without at least some knowledge about how to code, you will be in the same situation as a person who have never learned reading or how to do math. You will be missing out on something amazing.
Never stop learning, and life will show you amazing things!