Does every web server have a key pair?
It is common for administrators to log into webservers using SSH with public an private keys.
But from the perspective of the user, it's not every webserver which has an own keypair but rather every website (which isn't a one-to-one relation. A webserver can host multiple websites and a website can be hosted by multiple webservers).
When the HTTPS protocol is used, the website will transmit a certificate with its public key. The certificate itself is also signed with a private key: the key of a certificate authority. Your webbrowser comes with the public keys of several trusted CAs. This allows your web browser to verify that the certificate is genuine and the webserver really represents the website it claims to serve.
The HTTPS protocol is a quite good example of different kinds of cryptography used in everyday situations. When you want an introduction to applied cryptography, then HTTPS is a good subject to study.
Every email address?
In a perfect world, every email address would be associated with a PGP keypair. But in the real world end-to-end email encryption is unfortunately rather uncommon. Pretty Easy Privacy is a new attempt to make encrypted email more common. The future will show if it will catch on.
Every personal computer?
Not per se, but there is usually several software on a PC which uses public key cryptography in one way or another. A key can represent a computer, a specific program, a user (human or non-human) or an unique identity of a user. But usually only in the context of specific applications.
Keypair cryptography is also used in UEFI to verify the bootloader of the operating system or a TPM module.
Every database server?
Just as with websites, it is good practice to use keypair cryptography for logging into a database server. But in every database system I ever worked with, encryption is optional.
Every mobile device?
The SIM card in every mobile device contains an unique key which is used to authenticate with the base stations (the authentication key). It's not an example of public/private key encryption, because there is no other key. The cellphone provider has a copy of the key on their own server.
In addition, modern smartphones are practically miniature personal computers, so the same applies regarding keypairs used by arbitrary applications. Android has an API which allows applications to create and store keypairs on the device and so does iOS.
Every Facebook account (or other online profile)?
It rarely makes sense to give each online profile an own keypair. When you have a website, then all communication between the accounts happens within your trusted systems, so authentication and confidentiality is unnecessary.
Every WhatsApp account?
Whatsapp now uses end-to-end encryption which requires a keypair on each device.