Yes.

Oh - you wanted a little more than that. ;)

There are two main variations - applications that run natively on your devices, and cloud-based managers.

The obvious advantage with cloudy ones is that you only need to know that one password, and you can access it from any computer that has an internet connection. The main disadvantages should be obvious, but I'll spell them out anyway: If it's cloud-based then, without an internet connection, you don't have access. And if the provider gets hacked, all bets are off; depending on the nature of the hack, the attackers could have access to your password database, so you don't just have a problem on one site/service/whatever, you have a problem with every one of them.

Looking at the ones that run on your computer, you still have the benefit of only needing to know that one password, but now you're limited to only being able to access it from the computer the data is on. It's on that computer regardless of whether you have an internet connection, though, so that's something. The password database should be encrypted, so as long as you make your main password strong (and keep it safe) if someone manages to access your computer, they shouldn't get those valuable passwords.

So with the risk of cloud being a disadvantage in one case, and the limitation of one PC being a disadvantage in the other, there's a compromise solution: Use one that runs on your devices, and store the database file on something accessible by them all.

If you were just talking desktop PCs, I'd suggest storing it on a network drive - but you mention laptops and phones, so you'll probably want access when out and about. In which case, Dropbox (for example). While that means you're storing the database file in the cloud, with a good manager it should be a locally encrypted file - so even if someone gets into Dropbox, they won't be able to get into that file.

This is what I do - though using Pcloud not Dropbox.

The program I use is called KeePass; it has official versions for Windows and Linux (including versions that can run from a USB drive, so you can plug it into any computer - but that's no good if you want more than one person to access the file). There are also unofficial ports to Android and iOS, so that's your phones covered. (Probably).