Using the right thread can make a big difference in your stitches! When I first started sewing, I bought whatever thread was on sale and lots of it. You couldn't keep me away from the 5 for $1.00 bin. I was a self-taught sewer and I figured the cheaper the thread, the more fabric I could buy. Big mistake!
Thread is made up of strands of fiber which is twisted into shape. The best thread to use is "long-staple" - it's made with a much longer fiber so it has a smoother finish. Threads are also specially finished to smooth them out. The fuzzier the thread, the cheaper it is and the worst it will look in your project!
The best thread manufacturers are Mettler and Guterman. They can be trusted to use the best long staple cotton and other fibers. I also use Coats & Clark for garments as their thread is very strong. For fun projects, I'm a fan of variegated thread and metallics.
When you buy thread, look at its fuzziness, test the strength (pull it between two hands until it breaks) and examine its smoothness.