My favorite author of all-time is legendary strength coach Dan John. Now, for those that are not in the strength and conditioning world, it's important to point out that he's much more than two first names. Besides being a Fullbright Scholar and a professor, Dan John is famous for being able simplify complex subjects to the point where a five year old could understand it. Suffice to say, anytime I read his work, I become a better coach, trainer, and person.
Currently, I'm reading his newest book, Intervention, and he has a great quote about the value of building overall strength:
"Absolute strength is the glass. Everything else is the liquid inside the glass. The bigger the glass, the more of everything else you can do."
I'm going to let that sink in a bit more. So read it again.
Ok, ready? No matter your goal, being stronger is going to help. Want to run a 5 or 10k? Getting stronger will help. How? Well, every time you take a step, energy is lost. However, the stronger you are, the more energy you're going to be able to return to your body, giving you a faster time. In fact, there's been studies that indicate how vertical jumps, as well as 50 and 300 meter sprint times are highly correlated with 10k finishing times (if you don't believe me, you can read the science here.)
Want to lose weight? You need to get strong to get lean. Getting stronger is going to tax your body, allowing you lift heavier and heavier weights. Taxing your body will also burn more calories during exercise and afterwards too.
If you want to perform better at a given sport or event, getting stronger will help. When everything else is equal (size, athleticism, skill), the stronger opponent will win every time. While there may not be a whole lot of science to back that point up, it simply makes sense.
Lastly, I'm not quite sure where this unfounded notion that lifting weights will transform you into Arnold Schwarzeneger came from. But, one thing I have noticed is that notion is usually spread by those who don't have worry about putting on "too much muscle." Heck, if putting on muscle was THAT easy, I'd be Mr. Universe.
I've said it before, not everyone's goal is to be able to make a 500 lb deadlift, bench press 300 pounds and so on. And that's ok! But realize that getting stronger WILL help with just about everything in your life...even carrying around your groceries.