No matter how short the hike, the following items are essential, not discretionary:
Bear spray. At $40 a can and available for sale in the park, it's not cheap, but it's a critical deterrent if you run into one. Know how to use it, too. Be aware that sometimes supplies are sold out.
Food and water. Your "meal" can be as simple as a protein bar and a bottle of water, but the properly prepared hiker has an energy-boosting snack, and it's just foolish to head out without some drinking water.
Appropriate clothing. Watch the forecast closely (available at every lodging office and visitor center). Bring a layer of clothing for the opposite extreme if you're hiking at least half the day. Yellowstone is known for fierce afternoon storms, so be ready with gloves, hat, and waterproof clothing.
Altitude awareness. Yes, this is rather intangible, but much of Yellowstone lies more than 7,500 feet above sea level, significantly higher than Denver. The most frequent incidents requiring medical attention are respiratory problems, not animal attacks. Be aware of your physical limitations—as well as those of your young children or elderly companions if they are with you.