Don’t sell Roboform short. Not only will it remember your passwords (and fill in the blanks for you automatically), but, in addition, it will remember other personal information in encrypted format AND sync all the info across your devices. Try it at …
Many say it’s the best password manager (and form filler) in the business! See for yourself.
Lastpass is worth a shot as well. Very much in the same ballpark. (I actually use roboform constantly and wouldn’t switch myself, but I’ve recommended lastpass to others and they’ve been pleased – it’s got some functionality in a free version while roboform is basically useless until you pay for it.)
LastPass is another great option to check out. Similar in some ways.
1Password is what I use. It is more expensive up front, but it is yours to keep and no subscription fees. The data is stored on your computer, encrypted, or you can store the encrypted data in dropbox or iCloud.
The best thing I like about 1Password is that they are VERY open to how their encryption works and what the current mainstream cracking programs are doing against their encryption.