This is the most troubling question I see on the Books & Authors section of Yahoo Answers, right after "Where can I download this book for free?"
But there's something sad and dangerous about the people asking if they're good writers. Because these are mostly teenagers. They post a bit of their writing and beg other teenagers for opinions. I don't click through, don't read the writing, but last night a young writer posed a slightly different question, and I answered. She asked if she should be worried if she thought her writing wasn't very good. And I said she should be glad.
Writing is not an inborn trait, like eye color. It is a craft, and it has to be learned. Too many people, writers included, think it is a mechanical ability you pick up in elementary school, and from there some people will be good at it and some won't be. The same idea attaches to art and sports and math.
None of it is true. Yes, some people might be physically taller or more mature and some people will have a higher natural intelligence, but you can have all the natural gifts available and still not succeed where it might be expected. If you do nothing, if you do not try, and fail, and learn, and try again, you'll go nowhere.
I wrote a script about Michelangelo a few years ago. I think he is the greatest artist who ever lived. And I tell you this, nobody in history has spent more of their waking life studying anatomy and drawing than Michelangelo. Ever. From early childhood until his stroke three days before he died, he was working at the basics of his craft. The only other thing he did was write poetry, and he was darn good at that, too.
Nobody would expect an athlete to reach the Olympics without a lifetime of training and competing. Well, maybe those curling guys, but you get the point. Nobody is good at brain surgery in third grade. Nobody is a skilled attorney in junior high. Why do they worry about being a good writer or not in high school? Yes, some are better than others, but that says nothing about where those folks might end up on the writing spectrum. If anything, I worry that being told you're good at writing too young may make you fear failure too much to change and grow.
If you're fourteen or fifteen or nineteen or forty-three, don't worry if you're good. Worry if you're not getting better. Read. Write. Repeat.
Learning to write is learning a craft. What's up on the anvil is your own head. Swing hard.