Check your layout design. I've seen this happen a number of times and it usually turns out that fields in the body of your layout have a pixel or two that've crossed the line into the header. Filemaker then treats the fields as part of the header and you get only one record showing.
Select all the fields in the body of your layout (in layout mode), and press the down arrow a time or two to "nudge" them down lower on the body. Check by entering preview to see if anything has changed.
Thanks for the suggestion. That makes a lot of sense, but it wasn't my problem. However, your suggestion got me poking around some more and I found the solution. For reasons beyond me it appears that the print dialogue box had the "print page 1 of 1" button highlighted by default, not "print all." I feel stupid, but didn't catch that minor but important detail.