KeePass

KeePass is a free open source password manager that keeps credentials in an encrypted database file on the user's own machine. There is no service, no account and no synchronisation unless the user arranges it themselves, which is the entire design rather than a limitation.

A local file is the strongest possible answer to the question of whether a provider can be compromised, because there is no provider. The database sits where the user puts it, and the security of the arrangement depends on the master password and on how the file itself is protected and backed up.

The responsibility that transfers is real and should not be minimised. Nobody can recover a forgotten master password, nobody backs the file up, and syncing it between machines is something the user sets up with a file sync service or a memory stick, which introduces the risks they choose to accept.

KeePass has a long history and a substantial ecosystem of independently written clients for platforms the original does not target. That ecosystem is a strength and a caution: the core is well scrutinised, while a third party client is only as trustworthy as whoever wrote it, which is a judgement the user has to make rather than one the project can make for them. The software is free.