[1] I find this easier than opening keepass and selecting the database from dropbox for some reason that might be as simple as dropbox having an easier to spot icon.
For my personal ones I'm keeping few algorithms in my brains. I'm using resource type (website/some server/device) and name (e.g. domain/model) as variables and after few steps in my head I always have different password for each kind of service.
Edit: I wrote SHA1-Pass, so I'm biased, but I know what you mean about having trust issues with closed-source password tools. That's one of the reasons I wrote it.
Is it this: http://manpages.ubuntu.com/manpages/natty/man1/sha1pass.1.ht... I don't see how you would use this the same way you'd use the other tools mentioned here. I can imagine a way, but it's no where near as convenient and still has it's own major usability problems.
What stops being hacked / keyloggered and them exfiltrating all your long, complex passwords?
After all, if my own system is compromised, I just get a lot of hassle. If LastPass ever gets hacked and leaks their passwords, they lose their business overnight. That's pretty good motivation for them to keep on top of their stuff.
I used to use 1Passwd, which stored the passwords in a local file, and that could be said to be marginally more secure, except that it generally uses something like iCloud or Dropbox to sync the passwords, so there's still a single point of failure... The main reason I moved away from 1Password was that they gave me a shitty response when I asked them if they were going to support Chrome. I decided at that point that I didn't want to give them my money anymore, and so I didn't upgrade to 1Password 3.
The key for your encrypted file stays in your head (and/or in your wallet), so even a full-on total breach of Dropbox/iCloud, your key is safe, and 8 million rounds of 265-bit AES and a good password (my current KeePass settings) is still unbreakable[1].
1: Unless (perhaps) you have the attention of certain governments. And they always have the option of using a $5 wrench on you, anyway.
[1] Or so they say. I've never MITMed their SSL, and their software is not open source AFAIK. This is not to say someone couldn't e.g. distribute a trojaned version of their browser extensions. If you poke around the developer(s) have at least revealed the encryption method for the your DB so you can verify how it is encrypted for yourself, which is a good sign if nothing else.
No. This is the strength of two-factor authentication, something you know, and something you have. If someone gets your 1Password keyfile, it's useless without your decrypting password.
Works excellently!