For sure!
When you are ready to start learning Object-Oriented Programming it might be easier to learn on Java or Ruby. But if you like programming definitely learn to program in C/C++ as well. Once you get good enough you will be able to easily switch between languages.
Here is a really fun tutorial that explains some good programming concepts and has comics:
http://poignantguide.net/ruby/
It is in Ruby, but it doesn't hurt to try that out as well.
I wish I could point you towards some good beginner C/C++ tutorials but I do not really know of any. I think the C++ for dummies book might be an ok place to start, but C/C++ can be really picky about certain things, so it might be better to get more comfortable in another programming language first (PHP, Python, Ruby, Javascript). Just try not to get discouraged and keep trying!
The first language I learned to program in was Scheme. It might put a sour taste in many peoples mouths... but I loved it. It is a great way to break your thinking style and force yourself to think in an entirely new way.
If you are interested in making games (most programmer's under the age of 30 are, and learned to program mostly because of this) You might want to check out some of these programs that are designed to teach programming concepts while making games and have a lot of really great in depth detailed tutorials.
http://www.gamemaker.nl/
http://www.garagegames.com/products/torque/tgb/
If you plan on going to college for Computer Science you will be ahead of the curve.
Come see me in 1 years time from now for more advice.