My daughter, who turned 7 last month, recently learned how to ride her bike without training wheels. I had spent a few afternoons running alongside her, trying to keep her from falling over. Then, I just left the training wheels on her bike, but high enough off the ground that she had to learn to balance even with them on.
My daughter was so excited when she realized that she could balance on her bike! I let her try without training wheels again, and she rode like a pro. Except for turns and stops, of course! Now all she wants to do is ride her bike.