Personal Seals

A person receives a package or is filling out a contract. However, there's a delay, because they can't find their Personal Seal. No, not an animal.

This may seem strange to Westerners, but Japan, like several other countries including China, does not actually consider a signature to be sufficient to complete a legally binding document. A person requires a specifically designed stamp, also called a chop, registered with the municipal offices, in order to identify themselves. These stamps, referred to in various contexts as hanko, inkan, mitome-in, or jitsu-in, and are usually used with red ink to mark a document.

The inability to locate one's inkan can be a delaying action to build tension or comedy, as appropriate. Alternatively, a person can accidentally stamp a document far more easily than they might sign one, leading to unintended results.

A similar practice was once common among European nobility, specifically through the use of signet rings to impress a personal seal into wax bindings on messages.

Examples of Personal Seals include:

Anime and Manga

Hand Maid May: Kazuya Saotome receives a package from the Cyberdyne Company, he needs to go look for his seal. When he turns around, however, the delivery person is nowhere to be found.
Please Teacher!: Kei Kusanagi is filling out forms to officially marry Mizuho, ostensibly to protect themselves from reprisals from his school. He is very hesitant about whether this is right to do, but a distraction takes the decision out of his hands, causing him to accidentally put his stamp on the paper.
The Cold Opening for each episode of Excel Saga usually has a scene of Rikdo Koshi's personal seal being used to signify his 'approval' of the contents of the episode, whether this is a Dating Sim, action movie, science-fiction movie, or whatever Nabeshin and company came up with for that week.
- It also features probably the most over-the-top usage of a stamp in anime: in one of the openings, we see a huge meteorite destroying an entire city and carving an enormous crater... and the meteorite turns out to be a building-sized version of Rikdo Koshi's stamp.
Despite driving like a maniac for her driving tests, Natsumi in You're Under Arrest gets a driving licence anyway, since the examiner passed out during the test, conveniently letting the stamp fall on the requisite box on the form.
Zeniba's golden seal in Spirited Away turns out to be a major plot point, and in one DVD special the English staff talk about the addition of the word "golden" to keep the mostly young audience from mistaking it for the other type of seal that barks and dives underwater, viewers being morons and all that.
- And since the seal is in essence Zeniba's name, her sister's theft of it is not just robbery, but an attempt to gain magical power over her.
A package being delivered, and the subsequent search for the seal, takes the place of the opening sequence in the first episode of Seven of Seven. It also allows us to see the deliveryman get totally freaked out, and prove that voice actors can count to seven and deliver Title Drops at the same time.
In one scene of Girls und Panzer Der Film, Miho's sister uses their mother's seal to authorize a transfer for Miho. The implication is that their mother is unaware of this.

Fan Works

When Doug Sangnoir uses his contacts to create a legal identity for Luna's human form in the Sailor Moon installment of Drunkard's Walk, among the materials she receives is a set of three seals. "Basically, you have one for day-to-day stuff, one for banking, and one for big official paperwork." In the concordance for the story, the author goes into a bit more detail about them for anyone who might be unfamiliar and interested.

Film

In the movie "A Taxing Woman" tax evaders use all sorts tricks to hide the extra personal seals associated with their hidden bank accounts.

Literature

Adron's personal seal is an important plot point in the Dragaera novel The Phoenix Guards.
An example of the western version appears in Dan Brown's novel Deception Point. Evil Conservative Senator Sedgewick Sexton places self adhesive wax seals on manila envelopes which contain "evidence" that the president was behind a vast conspiracy to... make it look like aliens exist to ~~make himself even more insufferable~~ impress the journalists he plans to hand them out to.
In Dune, the signet ring of House Atreides is mentioned.