I am trying to build a form which uses a field that can self-expand, i.e. is not constrained by set vertical boundaries. For example, if I enter one word into the input field, the resulting field is one line high. If were to I enter a list of items numbered 1-10 or if I enter a long string or paragraph that wraps 10 times, the field adjusts to be 10 lines high.

Is this possible in FileMaker?

This is not possible in FileMaker. What FileMaker does have the ability to do is shrink the size of the field when previewing or printing. This is done with the Sliding Objects feature. It allows you to set the size of your field to the largest possible data content and then slide through the unused space on a record by record basis. You'll find the Sliding Objects feature while in layout mode under the Format menu.