I recommend you start boxing if you're looking for a fun way to stay fit and challenge yourself. As far as going pro, you would really need to have 1 in 10,000,000 talent in order to have a chance at being really sucessful at this stage in your life. There are a few reasons for this: First, the kind of stamina you need in professional boxing is developed over years and years of training. It's not just a matter of being in shape because it involves a lot of other skills that take time to develop. You need to breathe regularly and relax in a fist fight, which does not come naturally and takes time to learn. There's other stuff too. You could be in Floyd Mayweather or Margartio shape and be winded after a few rounds if you don't know how to do those things. I won't tell you that it's impossible to turn pro, but the odds of making any real money or even having a televised fight are long indeed. Basically, I would tell you something similar to what I'd tell someone thinking about starting their own business. Don't quit your day job until you're sure you can be successful. It's very hard and the majority of people aren't cut out for it. To use another business analogy, putting on gloves for the first time at age 26 and trying to make it to the top in boxing is like trying to start a chain of supermarkets without ever even owning a convenience store. I guess what I'm saying is that if you're going to take up boxing with the goal of turning pro, you shouldn't. I say that because it's simply a flawed approach to learning something. If turning pro is all that's important to you then you're in no shape to mentally handle what's involved on the way there. You should start boxing only if you think you'll really enjoy it. If you go in with the goal of improving your skills and your physicality each day, you will get a lot more personal satisfaction and you will go as far as your ability takes you without being disappointed. Also, I'm sure someone else mentioned this, but know the risks. You can get seriously hurt if you fight someone you're not ready for.
26 isn't too late. You might be a little too late to have very many pro fights if you ever got that far, but you've still got time for a good amateur career at least. Even if there's no chance of success, there's nothing to stop you from going down to your local boxing gym and training and doing something you really want to do. You'll meet some cool people, get in shape, and have some fun and being a late starter shouldn't stop you from at least doing that.
try doing some sparring in your local gym first...just to see how you'd do with the average person (one with atleast basic knowledge of the sport). Hitting hard is not a guarantee to success...movement plays a bigger role imo. Go ahead! just make sure you have fun doing it!