The excellent 1Password stores more than just passwords. It has prebuilt templates for keeping other kinds of sensitive information as well.
KeePassKeePass comes in two variants: the classic edition (version 1.21) and the professional edition (version 2.18). The differences between the two mainly revolve around compatibility with different versions of Windows and the breadth of available features. You should use the 2.x branch whenever possible (I've used both and I prefer 2.x), but the 1.x branch works fine and will be kept up-to-date for the sake of cross-compatibility.
When you create a new database in KeePass, it comes preloaded with a number of possible categories for passwords: Internet, email, home banking, and more. These categories are user-editable, and you can do without them entirely if you want, but I found them useful. Aside from the master password, you can also set the number of encryption rounds to use. The more rounds you set, the more secure the encryption, but the higher the CPU cost when you unlock the database.
Each new password entry comes with a randomly generated password, and the rules for password generation are user-editable. You can either opt for that password as-is, replace it with an existing one, and even set an expiration date for it so that you're reminded to replace it periodically. The cryptographic strength of a password is indicated by a color meter, in which red means weak, green means strong. If you change a password, the previous version is kept in a backup directory (in 1.x) or in a history tab for the password entry itself (2.x).
If you assign a URL to a given password, you can have the accompanying username and password automatically filled in whenever you visit that site with a Web browser and press a customizable key combination. The exact sequences of keystrokes sent can be customized for each website -- for instance, if you're dealing with a site that has a log-in box where the Tab key doesn't take you from the username to the password field. Other keystrokes let you copy just the username or password to the clipboard as needed. You can also use a number of plug-ins to allow tighter browser integration, but the program's default behavior was more than good enough for me.
KeePass also has security features that extend outside the program. When a password is placed in the clipboard, KeePass automatically blanks the clipboard several seconds later (you can set the interval). The program can be set to accept its master password via the same secure desktop environment that Windows itself uses for UAC, which makes it harder for a third-party program to hijack input.