Recs.
Updated
KeePass is a free password manager that's available for Windows, with unofficial ports for other operating systems.
SpecsUpdate
Pros
Pro Powerful built-in password generator
Password generator can be adjusted to use or exclude certain characters, patterns, external algorithms and principles.
Pro Extensive plugin and extension support
Keepass offers a range of plugins and extensions in different categories: Integration & Transfer, Automation & Scripting, Cryptography & Key Providers, and others.
Pro Allows storage of attachments such as pictures, documents and all kinds of files in general
Appending attachments to individual credential entries allows things like scanning important documents (for instance a scanned document containing the login information for your internet connection), appending them to the corresponding credential entry and afterwards destroying the original paper copy.
Pro Offers multiple sync options
Since the database is stored locally it can be synced across devices using a cloud storage service like Dropbox, Google Drive or via a file sync tool like BitTorrent Sync. KeePass v2 also provides a powerful built-in synchronization mechanism that allows setting appropriate level of sync, kind of sync, and choosing between a number of sync sources (Dropbox, Drive, etc).
Pro Built-in history that tracks changes to individual credential entries
With the built-in history you can lookup previous passwords, track changes in general and if necessary recover those. In essence you are looking at a built-in Version Control System (VCS) which operates on single entries. Browsing the history of specific entries also displays associated metadata like the date of a change.
Pro Customizable password records
Users may define any extra fields (eg. "Surname", "Credit Card No", "Start Date", "Expiry Date" and "Security No") and their values may then be easily copy-and-pasted when required. This is a great feature not found in a lot of password-managers: they leave you to consign such additional information to the "Notes" section.
Pro Clear, concise user interface
This app has the easiest, cleanest, and clearest user interface. For reference, LastPass has progressively gotten worse and worse and is now a confusing mess, while Keepass remains very user-friendly.
Pro Works inside Android apps
There are variations in support of features, so this is dependent on the Android app being used. Keepass2Android is one that has built-in synchronization over ssh and other protocols, fingerprint support and plugins are also supported to a certain extent.
Pro Support in iOS Safari browser
Difficult passwords are mostly a PITA on a mobile keyboard.
Cons
Con Officially supported only on Windows, Mono or Wine
While there are ports available for Linux, OSX, iOS, Windows Phone and Android, the only officially supported version of KeePass 2 is on Windows and all platforms running Mono like Linux, Mac OS X, BSD. KeePass 1 is supported on Windows and Wine.
Recommendations
Comments
Flagged Pros + Cons
Con Uses a database
Uses a database and thus decrypts all passwords within it when only one is needed. Which is less secure than having individual files. It also means you will have only one master password.
Pro Powerful built-in synchronization mechanism
KeePass v2 has a built in sync mechanism that allows setting appropriate level of sync, kind of sync, and choosing between a number of sync sources (Dropbox, Drive, etc).
Con Only local use
Useless app for people who need access to their login information anywhere else. No access on android/iOS, no web access, no backup, nothing but 1 local database (unless carried around on a USB plug - which can easily be lost or forgotten).
Con Possible security vulnerability
There is a possible vulnerability with the way the app does updates in that the update files are transferred over HTTP. While no one has reported a breach yet, the possibility of it could be a concern.