Recs.
Updated
SpecsUpdate
Pros
Pro Automatic cloud backup and cross-device sync
LastPass keeps an encrypted copy of all passwords locally as well as an encrypted copy on their servers. That way, passwords can be accessed locally while offline, or through their server while online from any machine. Linux, Mac, Windows, Android, iOS with integration for Chrome, Firefox, Safari and possibly other browsers
Pro Offers multiple export options
LastPass can dump the whole database as a .csv file or an encrypted file that can then be decrypted using LastPass Pocket as well as separately export Wi-Fi passwords and autofill information. Additional export options are available on a per-browser basis.
Pro Works with portable versions of Chrome and Firefox
Firefox 2+ on Windows, Mac & Linux as well as Chrome 4+ on Windows and Linux support a portable version of LastPass. Great for securely accessing LastPass Vault from public or untrusted computers.
Pro Multifactor authentication
LastPass offers multiple multifactor authentication options, including Google Authenticator, Grid Multifactor Authentication, Microsoft Authenticator App, Toopher Authentication, Duo Security Authentication, Transakt Authentication, Sesame Multifactor Authentication, Smart Card Authentication and Yubikey Multifactor Authentication.
Pro Seamless autofill and password generator via plugins for all popular browsers
All common browsers, including Opera, have plugins that allow automatically filling in forms and generating passwords. All form fill information syncs across all platforms, devices and browsers. Password generator can be adjusted to use or exclude certain characters and patterns.
Cons
Con Very bad UX for sharing passwords with other people (in free version)
When on lastpass.com you update the contents of a password file, it gets updated only on your side, not on the side of people it is shared with (and the UI does not tell you anything about this).
Also, when you want to share a password file with someone, they often have trouble accessing it (bugs in registration or acceptation of the shared document).