One of the things I really love about programming is that I love learning new things, and programming is a great medium for working in ideas. Once programming becomes simply work, the spark is gone and it's better to go find something else to do.
Almost 20 years ago I taught myself C, which I really liked a lot at first. That programming language has some ideas that were pretty interesting to me coming from BASIC, but it became clear to me after a while that C programming is more about twiddling the drudgery bits and details than it is about expressing ideas. Don't get me wrong, C is great for certain things. If I were an operating systems builder I probably wouldn't use anything else.
I don't program in C anymore, but I wouldn't discourage BASIC programmers from learning C or any other language. I learned a lot of ideas from my experiences with C, Forth, Smalltalk and Java. There's no substitute for trying a new language. Even if you still only use BASIC it will change your programming style when you are exposed to new ideas, and you will also have more fun.
Learning. I heartily recommend it. :-)