Possible substitutes for paprika include cayenne pepper or chili powder. Paprika is a mild spice, and substitutions of hotter peppers should be used in reduced quantities.
Paprika is a red, powdered spice made from sweet peppers. Hungarian paprika, which is mild and sweet, is the gold standard of paprika. Other types, however, are available. Some are smoky and some are even hot. One popular type of paprika is called pimentón dulce, which is produced in Spain. Different types of paprika can be substituted for each other in a recipe, resulting in a slightly different flavor profile.
Some other spices can work, too. Substitutions depend on what kind of paprika was called for in the original recipe. Most likely, it was a mild, sweet paprika. In this case a mild chili powder, such as ancho, is a good choice. Chipotle powder can be used to replicate a smokier paprika. For a hotter substitute, cayenne pepper can be used. Cayenne pepper is extremely spicy, and most recipes need no more than a pinch.
Other potential substitutes are black pepper, Cajun spices or even a mild hot sauce. One of the benefits of actual paprika, however, is the appearance it lends the final dish. Bright red paprika is often used on deviled eggs, and is as much a garnish as a flavor enhancer.