Recent events in the industry concerning security forced me to rethink my password handling strategy. It's been due for a long time, but I somehow always managed to evade it :-) This changed after an old buddy got his Iphone hacked. Additionally, Dropbox hack proved to be the real thing. As if that was not enough, even Yahoo admitted to being hacked back in 2014.
Now, having the same password on almost all websites such a situation might prove problematic. But dealing with different passwords on each and every website where you need to authenticate is a hassle. That's where Password Manager comes in.
Being an open source supporter, KeePass seems like a solid choice. Mature product with good reviews from virtually everybody. The application will create an encrypted database, storing all your passwords. The trick is to remember only one really complicated password which will unlock your database.
There are also a lot of goodies in the form of plugins. For example you can install IOProtocolExt plugin, which lets you synchronize the password database among multiple devices using the SSH protocol. Or alternatively, you can use KPDataSave (Dropbox) which lets you sync the database through Dropbox. Theoretically speaking, the password file could be accessible to anyone, as it is encrypted with your hopefully very complicated master password.
I also found KeePassDroid, which is able to read the pasword files, but unfortunately haven't yet found the time to check it out.