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Updated
LastPass is a password manager that simplifies everything you do online by remembering your passwords, logging into your sites with one click, creating strong passwords for every account, and so much more.
SpecsUpdate
Pros
Pro Strength of strong, unique passwords without needing to remember them
LastPass uses a single master password to keep the rest of your unique passwords safe. All you need to do is remember your master password, and you will be able to log into any website which LastPass remembers. This means that you can have a different unique password for each website you use (which is highly suggested) without needing to remember them (once you enter your master password, LastPass will auto-fill the password for the website).
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 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).
Con Web Extensions in FF are partially broken, signs of issues in Chrome; updates are few and far between.
For a PW manager that is entirely web based, this is kind of a deal breaker. And to make matters worse, LogMeIn/LastPass often blame Mozilla and/or Google for not processing update submissions fast enough. Other extensions don't have this issue, so why do you?