I use RoboForm:
http://www.roboform.com/ Works great on Android, as well. Can't speak for iOS, but I assume it's just as good.
RoboForm's syncing is very good, and it gets updated regularly, which is nice, considering the velocity of browser updates. I also really like its password generator, very flexible, very configurable (types of permitted/required characters, number of characters, etc.).
More than once, I've needed access to an account from my phone. No chance I'd ever remember strong passwords, so having RF on my phone has been a life-saver.
I have well over 100 logins saved in RF. No way I could keep all of that straight in this ol' brain.