Ha! I have this comic posted on my cubicle wall: http://xkcd.com/936/
It's friggin 2014... why can't they just scan my eyeball?
Except that comic is totally wrong. Before password crackers use brute force (guessing every possible combination) they use "dictionaries" that try words and combinations of words.
If you find the idea of password cracking even remotely interesting, check out this Wired article:
http://www.wired.com/2012/11/ff-mat-honan-password-hacker/all/
The comic is spot on, but they should have mentioned diceware (
http://world.std.com/~reinhold/diceware.html). The entropy isn't due to the number of letters (brute force), it's due to the length of the wordlist. With diceware you use a list of 7776 words and 5 dice to randomly choose them (each roll of 5 dice gives you one word). Even if the person trying to guess your password knows you used diceware this still works, and you should always assume the bad guy understands your methodology in choosing your passwords, because we are rarely as clever and unique as we think, and they are better than you'd expect. If your password wouldn't stand up if your method in choosing was known, it's a bad password. With 4 diceware words like in the comic, that is 7776^4 possibilities to guess. At 1000 guesses/sec (which is too low by about a million), that's 115k years.
7776^4/1000/60/60/24/365 = 115936.02
4 words are no longer good enough, you'd want 5 minimum, 6 ideally, but the idea in the comic in still very valid.
To the original question: Lastpass, keeppass or 1password are all good options. I use 1Password but only because I'm on a Mac. Whatever you use, make sure your master password is good.