I had an account on a website, but don't remember which one
Search your email account for an account creation confirmation email. Helpful search terms may include "bitcoin", "wallet", "exchange", "btc", "blockchain", or "cryptocurrency". If you purchased bitcoins, you may want to look at your old bank statements as well. There is no global register of bitcoin users or services, so if you cannot find anything you may be out of luck—we cannot help you, because we don't know either.
I had a web wallet, but the service shut down since
If the service had custody of your bitcoin balance, it is likely lost. Research the name of the service to determine what happened to the service, in case it just rebranded and is still around.
My wallet service still exists, but I lost access
We don't have insight into your customer relationship with services, so we cannot help you. Contact the service and initiate an account recovery process.
I had a self-custodial wallet, have lost the wallet, and have no backup
Bitcoin balances are tracked via the blockchain, and a user's bitcoin wallet's primary purpose is to secure the private keys which are used to establish ownership and to track any transactions related to those keys. The key space is enormous. If you have lost your wallet, the same keys will likely never be regenerated and no one will ever be able to spend the associated funds.
I had a self-custodial wallet, and still have the device that it was installed on
Looking over this selection of wallets may help you remember which one you used. If you still have the wallet files, you may be able to recover your funds. The name of the relevant files depends on the software that you used, but one of the most common file names is wallet.dat. If you find a wallet file, create a backup first before trying to recover the wallet.
I have a 12 or 24 word backup, what do I do?
This is called a mnemonic seed phrase. It is a standardized way to backup a wallet's private keys. Keep the words confidential, do not enter the words in a website or untrustworthy software. You should be able to recover your wallet from the phrase. You can find instructions how to recover the wallet from it on this site.
I had a bitcoin card purchased from a drug store¹ many years ago
Without knowing the details of the card or the business that created the card, it will not be possible to recover control over any money associated with the card.
¹ Inspired by lost bitcoin card purchased from a drug store many years ago