Shock the reader with an unexpected fact or claim to get her attention. For example, an introductory paragraph about mosquitoes might begin, "Small in size but packing a powerful wallop, blood-sucking mosquitoes may be responsible for more human deaths worldwide than any other creature."
Relate a funny story to pull a reader into your topic. For example, an article about cooking might relate a cooking flop that involved using salt instead of sugar or burning dinner to the point where the charbroiled chunk was unrecognizable.
Ask a thought-provoking question to encourage readers to think about your topic. For example, ask readers a question such as, "Why do you favor certain colors and patterns above others?" Expand on the question by giving readers a tidbit about what occurs in the human brain to determine style and color preferences.
Give a foreshadowing hint that readers will understand later. This can especially effective in fiction writing. For example, you might write, "George always hated it when his brother called him 'Shorty'." Later in the story, George may grow taller than his brother and resist the urge to use the same name for his brother.
Begin the paragraph with startling dialogue. For example, you might start a fictional story with, '"Barnabus!" The deep bellow of the old man broke the early morning silence and the small boy scrambled to hide from sight."