I'm using random generated passwords by keepass. More due to laziness, than for having stronger passwords. I don't want to remember multiple passwords!
Your both correct, and incorrect. For that model of hacking, yes it works.
However, if they're hacking like that, with simple incrementation of lettering, then you can rely on account lockouts really. No, they don't work like that.
They work off both looking for words & doing incrementation. Plus, with the sites that have a 3-guess-limit, it'll probably be a human attempting it, purely as they have a better chance of getting in than a computer within 3 guesses.
So, the solution is to organize your passwords. By having random number/symbol replacements you automatically make it harder for a human or logical guess algorithm to guess, and making it say, a short sentence, makes it slightly more challenging for a simple incrementation.
You make sure then that you follow a rule on all your passwords as to how you replace letters, so it might be that you just replace every o with a 0. I knew someone who did that in the chat of games, without flaw, and it took them a while to move out of that habit after they changed usernames (as the replacement linked to their username, which also replaced o's with 0's).
Then you only have to remember a rule, and a memorable (not random, as random words don't matter to computers on simple incrementation) word/phrase. E.g. the country of your favourite holiday destination + your favourite restaurant there.
Just in case you don't get simple incrementation & logical guessing:
Guess 1: aaaaaaaaaa
Guess 2: aaaaaaaaab
Guess 3: aaaaaaaaac
Guess 4: aaaaaaaaad
and so on.
Logical guessing, uses information already obtained to make an educated guess (Yes, a computer can kind of do this...)
Firstly, it may use say, your twitter posts, and use words (possibly filtered by wordlength and type to eliminate words like "and") to guess,
Alternatively it may work off known popular passwords or phrases, and slowly work its way down the list of popular words/phrases.
Normally a combination of the methods is used, and I'm sure there is other ways of cracking passwords.