The received wisdom states that if you don’t blink when you sneeze, your eyes will fly out of your head. Thankfully, as is often the case with urban legends, this theory is a load of hooey. Your eyeballs are safe and sound in their sockets. For a funny pictorial representation of this hypothetical scenario, check out this urban myth page from MTV.
In reality, a sneeze is simply an involuntary nervous response to nasal irritation. According to this nifty science blog entry, the sneeze impulse affects a variety of body parts, including the abdomen, chest, neck, and face. During a sneeze, the impulses that travel through your face cause your eyelids to blink. This response is entirely automatic. There’s nothing you can do about it. Sneezing puts a lot of pressure on your head and respiratory system, so blinking is probably a protective mechanism.
The point is that all of these responses (the abdominal contraction, the sharp burst of air out of your lungs, the general lunging movement) are intertwined. When you sneeze, you can’t do one without the other.