The KeePassX database file is securely encrypted, so if anyone gets it, it does no good without the master password. Pick a good, secure master password and you don't need to worry about it. With only one to remember, you should be able to do that. I have mine in my Dropbox folder, so I can access it on any of my devices, including my Android phone and tablet, and any changes are automatically synced to all devices. If anyone breaks into Dropbox, all they can get is an AES-encrypted file, not actual passwords. Decryption is done on each individual device, and stays decrypted only for the time set in the settings, one minute in my case. After that one minute, the file is automatically encrypted again and I have to enter the master password again to get the passwords. KeePassX will also generate a pseudo-random password of any desired length, using any combination of characters you specify. I have no idea what most of my passwords are, and don't care. I know one master, which I can change at will, and that's all I need. I've been using a password safe for years, and have hundreds of passwords in there. I can't lose the file, because it's in multiple places, on all my computers and on Dropbox, encrypted on all of them.

Another possibility is LastPass, which integrates into your browser, and logs onto websites automatically for you, after you enter the master password. I'm not as big a fan of that, because although convenient, I'm not sure I trust it completely. KeePassX is open-source, and I know the passwords are not stored anywhere in the clear.