My puppy sure seems to hiccup a lot these days.  Is this normal?

A temporary spasm of the diaphragm.

It is completely normal for a puppy to have hiccups off and on throughout the day. Hiccups sometimes start after eating a meal, but can occur at any time and last for up to several minutes. A hiccup is defined as a non-controllable spasmodic contraction of the diaphragm, causing a beginning inspiration of air that is suddenly stopped by closure of the glottis. The diaphragm is a muscle that separates the chest from the abdomen. It enables the lungs to bring in air during inspiration. When the diaphragm contracts, the air is quickly drawn in, but the glottis, a part of the "voice box," suddenly cuts it off.

Puppy hiccups will come and go. Eventually puppies grow out of them.