Short of a CPAP machine and weight loss to reduce the pauses in breathing that sleep apnea sufferers experience, this study found that mouth and throat exercises were remarkably effective at improving breathing, reducing snoring, and reducing daytime sleepiness and mood swings (those related to poor sleep at least).
Since sleep apnea is now known to contribute to high blood pressure, insulin resistance, diabetes, and heart disease, there's the chance that going through these motions could add years to your life, if not improve its quality:
Effects of Oropharyngeal Exercises on Patients with Moderate Obstructive Sleep Apnea Syndrome, American Journal of Respiratory and Critical Care Medicine, 2009
The second page of the study details the actual exercises. In brief, they involve combinations of sucking, swallowing, chewing, breathing, and speaking. Oh, and tongue brushing (with a toothbrush). For about 30 minutes a day in total.
Here's a video that accompanied the article: