From Bulbapedia, the community-driven Pokémon encyclopedia.
Footprints are the tracks left by a Pokémon. Each Pokémon has a unique footprint that is displayed in the Pokédex of every game since being introduced in Generation II. However, this is only applied to Pokémon with visible legs. Out of the 649 Pokémon in Generation V, 150 do not have a footprint. They are not featured in the Generation VI games, likely because of the full 3D view of the Pokémon.
In the games
When a Pokémon is caught, its footprint is included in the data added to its entry and can be found on the first page. For those without a footprint, the area footprints are displayed on remains blank.
At the start of Ruby and Sapphire, a School Kid initially blocks the entrance to Route 102 as he thinks he has found the footprints of a rare Pokémon there. It later turns out that they were his own.
In the Altering Cave of FireRed and LeafGreen, footprints may be found as well.
Dr. Footstep on Route 213 in Sinnoh is a footprint expert, and can evaluate a Pokémon's friendship simply by looking at its tracks. He will hand out a Ribbon to Pokémon with a high friendship value. Even Pokémon who do not have a footprint can be tested to get the Ribbon. Dr. Footstep has four different ratings on Pokémon friendship. These reflect the amount and size of hearts shown on the Friendship Pokétch application. The quotes vary depending on which Pokémon is being examined. Different Pokémon have different sets of responses, such as Ghost-type Pokémon saying that they are scary and shunned, and inorganic Pokémon such as Magnemite only make the noise "Sssshhnnn". If a Pokémon receives a Level 4 rating, Dr. Footstep will award it a Footprint Ribbon.
Wigglytuff Guild in Pokémon Mystery Dungeon: Explorers of Time and Explorers of Darkness judges a Pokémon's worth by its footprint. Before being allowed to enter, a Pokémon must stand on a grate in front of the guild entrance and have their footprint identified. Visitors or Guild members have to step on the grate to let the sentry (usually Diglett) verify whether they are wanted Pokémon. At a couple of points during the storyline and at any time after graduating, the player takes part in this sentry duty. It plays out as a mini-game where a series of Pokémon must be identified by their footprints, though more clues are provided over time. The game also notes the Pokémon who lack footprints in the scene where Dusknoir visits the guild.
In the Wi-Fi Plaza, there are two long boards that several people can get access to. On these boards, the player has the ability to select one of six footprint types. Once the type has been selected, touching the canvas with the stylus can place footprints at will. The other people will also be doing this. The footprints will quickly go and walk off the canvas after the player has placed them.
Pokémon Dream World
In the Pokémon Dream World, when a player visits another's home, they leave the footprint of their Pokémon on the Footprint Mat. Clicking these footprints provides information about the visitor. They will flash when the visitor has made a Dream Pal request.
In the anime
Footprints have been seen in the anime. In Hello, Pummelo! footprints of the Pokémon team used by the Champions of the Orange League are seen. As of the next episode, Ash's Pokémon's footprints are seen as well.
In The Unbeatable Lightness of Seeing! when Ash was feeling down after his loss against Brandon, he was cheered up when he saw a poster of his Pokémon's footprints.
In Mega Revelations!, Korrina was shown having collected footprints of the Pokémon she and her Lucario had defeated together. After defeating Ash and his Pikachu, she also had Pikachu add his paw print to her collection.