I'm trying to succinctly describe something that occurs most frequently, and the only single-word adjective I can think of is "commonest", but that sounds ridiculous. Are there any other good adjectives I could use?
From the Wikipedia article on Mode:
In statistics, the mode is the value that occurs most frequently in a data set or a probability distribution. In some fields, notably education, sample data are often called scores, and the sample mode is known as the modal score.
OP is not alone in thinking commonest doesn't sound so good today. It used to be a perfectly common word, but over the last century most common has become much more common. But if OP is determined to have a single word, there's nothing to stop him using the older form.
The other answers citing "common" or "prevalent" make sense, even without adding "most". If something is the prevalent method, then it is automatically the most prevalent method. The word "most" doesn't add any additional information, so may be removed.
On the other hand, if something is a prevalent method, then there may be more than one prevalent methods. So make sure you use "the" rather than "a".