KeePass

Website
Wikipedia
The original. There's many flavors that all do the same thing--- different features and functionalities, and different security implications too. Some allow plugins or web connectivity, some don't. Potato potato.

KeePass (2) is what my work laptop uses.

Flavors

KeePassXC

KeePassXC

Website
This is the software I use on desktop computers, and have for a long time. It's feature rich. The database can be synced across devices using various methods like rsync, cloud storage, or self-hosted solutions.

KeePassDX

KeePassDX

Website
Another Open Source KeePass flavor for Android. Installable from F-Droid. Comes with a keyboard and web features to inject username and password in appropriate fields. Historically kind of buggy because of the mobile environment - the way URLs work on mobile with apps and browsers is frustrating and sometimes it doesn't pick up.