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Information Security Stack Exchange is a question and answer site for information security professionals. I've always been an advocate of long rather than complex passwords, but most security people (at least the ones that I've talked to) are against me on that one. All too often, when discussing complex passwords, strong policies, expiration, etc (and, to generalize - all security), we tend to focus overly much on the computer aspects, and skip over the human aspects. Especially when it comes to passwords, (and double especially for average users), the human aspect should often be the overriding concern.
For example, how often does strict password complexity policy enforced by IT (such as the one shown in the XKCD), result in the user writing down his password, and taping it to his screen?
And I think that is the core message from the sage of XKCD - yes, Easy to Guess is bad, but Hard to Remember is equally so.
Edit: there seems to lack a thorough explanation of the mathematics in this comic (at least not as detailed as it could be), so here it is. The password generation process for this method is: take a given (public) list of 2048 words (supposedly common words, easy to remember).
For the letters which are eligible to "traditional substitutions", apply or not apply the substitution (decide randomly for each letter). The random word is rated to 16 bits by the comic, meaning uniform selection in a list of 65536 words (or non-uniform in a longer list). Uppercasing or not uppercasing the first letter is, nominally, 1 bit of entropy (two choices).
For the extra punctuation sign and digit, the comic gives 1 bit for the choice of which comes first (the digit or the punctuation sign), then 4 bits for the sign and 3 bits for the digit. If the choice of digit is not made by a human brain but by an impartial device, then we get 3.32 bits of entropy, not 3 bits. Four bits for punctuation are a bit understated; there are 32 punctuation signs in ASCII, all relatively easy to type on a common keyboard. The grand total of 28 bits is then about right, although it depends on the precise details of some random selections, and the list of "traditional substitutions" (which impacts the average number of eligible letters). The paragraphs above show that the maths in the comic are correct (at least with the precision that can be expected in these conditions -- that's a webcomic, not a research article). Bottom-line: even if you keep your method "secret", it won't be that secret because you will more or less consciously follow a "classic" method, and there are not that many of those.
Note that "hard to guess" and "easy to remember" do not cover all that is to say about password generation; there is also "easy to use", which usually means "easy to type". The comic assumes that the selection of a random "common" word yields an entropy of about 11 bits -- which means that there are about 2000 common words. The same users will probably complain about the hassle of typing a long password (if the typing involves a smartphone, I must say that I quite understand them).
Strength: Reasonable - This password is fairly secure cryptographically and skilled hackers may need some good computing power to crack it. Strength: Strong - This password is typically good enough to safely guard sensitive information like financial records. It is certainly true that length, all other things being equal, tends to make for very strong passwords -- and we're seeing that confirmed here. Even if the individual characters are all limited to [a-z], the exponent implied in "we added another lowercase character, so multiply by 26 again" tends to dominate the results. Therefore I say the cartoon is materially accurate in terms of its math, but the godlike predictive password attacks it implies are largely a myth. But I see more of a consensus that web site operators can't keep their hash databases secure over time against attackers, so we should engineer the passwords and hash algorithms to withstand stealing the hashes for offline attack.
This makes the problem even harder, and sites should really be looking at options besides requiring users to memorize their own passwords for each web site, e.g. But good password hashing can also be done via good algorithms, a bit more length, and bookmarklet tools.

Using the first password, I've got a Post-IT note in my wallet (if I'm smart) or in my desk drawer (if I'm dumb) which is a huge security risk. Lets assume that the pass phrase option is only as secure as the munged base word option, then I'm already better off because I've eliminated the human failing in password storage.
Maybe we should just introduce graphical passwords, where you have to draw the horse and battery staple in the final frame image. We all need strength to courageously face the various challenges of our lives, and so strength tattoos can act as a form of inspiration for us. That is a direct result of focusing too much on the computer aspect, at the expense of the human aspect.
His answer shows why the xkcd got the math right, a perfect complement to why it doesn't actually matter. But I think it is better for someone who would have difficulties in remembering a good password than choosing something trivial, like the name of their dog. If you have two password halves that you generate independently of each other, one with 10 bits of entropy and the other with 12 bits, then the total entropy is 22 bits. Choose four random words in this list, uniformly and independently of each other: select one word at random, then select again a word at random (which could be the same as the first word), and so on for a third and then a fourth words. These traditional substitutions can be, for instance: "o" -> "0", "a" -> "4", "i" -> "!", "e" -> "3", "l" -> "1" (the rules give a publicly known exhaustive list). There are more words than that in English, apparently about 228000, but some of them are very long or very short, others are so uncommon that people would not remember them at all. If the user makes that choice in his head, then this will be a balance between user's feeling of safety ("uppercase is obviously more secure !") and user's laziness ("lowercase is easier to type").
Other words could have other counts, but it seems plausible that, on average, we'll find about 3 eligible letters. But that's close enough for illustration purposes (I quite understand that Randall Munroe did not want to draw partial boxes). The maths in the comic are correct, but the important point is that good passwords must be both hard to guess and easy to remember. Long passwords are a problem on smartphones, but passwords with digits and punctuation signs and mixed casing are arguably even worse. An unhappy user is never a good thing, because he will begin to look for countermeasures which will make his life easier, such as keeping the password in a file and "typing" it with a copy&paste. In other words, will they actually attempt common schemes like "dictionary words separated by spaces", or "a complete sentence with punctuation", or "leet-speak numb3r substitution" as implied by xkcd? I expect it will be braindead brute force all the way to get the low-hanging fruit, and the rest ignored.
Which means, IMHO, that these specific two passwords are kind of a wash in practice and would offer similar-ish levels of protection. But I think the controversy is less around that, and more around how much entropy you want to have. In most of them, nobody would notice if I dumped a copy to a file and walked out with it, reversed those short, irrelevant passwords that users have handily re-used on other sites, then went from there.
If you allow weak passwords or strong ones, people use passwords in patterns, like youtotallywouldnotguessthis01 then youtotallywouldnotguessthis02. Usually you're protecting yourself from remote attacks, not someone sneaking around on your desk (that is an issue for office security). With this beautiful name necklace, you can provide two names, separated by a heart, displaying your love for all the world to see!
I did roll a couple of times to find a sequence that felt nice to say (in my head) though, without necessarily making sense. If we were to use a non-logarithmic scale, we would have to multiply: 210 uniform choices for the first half and 212 uniform choices for the other half make up for 210·212 = 222 uniform choices. This depends on the list of "traditional substitutions", which are assumed to be a given convention.

Among psychological factors, "0" has a bad connotation (void, dark, death), while "1" is viewed positively (winner, champion, top). You must convince them to use a device for good randomness (a coin, not a brain), and to accept the result.
The main message of the comic is to show that common "password generation rules" fail at both points: they make hard to remember passwords, which are nonetheless not that hard to guess. The thinking there is wrong, but I think dictionary attacks need a mention just to nay-say the naysayers and clear up the confusion here.
If there isn't any low-hanging password fruit (and oh, there always is), they'll just move on to the next potential victim service. And for Thomas those are multidimensional cross product operations, and I am assuming a right handed coordinate system in Euclidean space. Database compromise by an external actor isn't the only reason for hashing passwords properly, or for users choosing strong passwords. Entropy is a measure of the average cost of hitting the right password in a brute force attack. In south China, "8" is very popular because the word for "eight" is pronounced the same way as the word for "luck"; and, similarly, "4" is shunned because of homophony with the word for "death". You can do "I" as the first word, and then after the heart, put someone or something that you love! This letter looks quite good on its own, and when combined with other designs, it becomes a piece of art itself.
We assume that the attacker knows the exact password generation method, including probability distributions for random choices in the method. The attacker will first try passwords where the digit is a "1", allowing him to benefit from the non-uniformity of the user choices. Even when they don't, people have Google and colleagues, and will tend to use one of about a dozen or so sets of rules.
If the users alter the choices, if only by generating another password if the one they got "does not please them", then they depart from random uniformity, and the entropy can only be lowered (maximum entropy is achieved with uniform randomness; you cannot get better, but you can get much worse). A password is not strong because it is long; it is strong because it includes a lot of randomness (all the entropy bits we have been discussing all along). Another way to create a strength tattoo is to just have the word “strength” written across a particular body part.
An entropy of n bits means that, on average, the attacker will try 2n-1 passwords before finding the right one. The comic includes provisions for that: "You can add a few more bits to account for the fact that this is only one of a few common formats".
Extra length just allows for more strength, by giving more room for randomness; in particular, by allowing "gentle" randomness that is easy to remember, like the electric horse thing. Whether done in thin shapes or bold lines, these tattoos look very stylish and meaningful in spite of being very simple. When the random choices are equiprobable, you have n bits of entropy when there are 2n possible passwords, which means that the attacker will, on average, try half of them. On the other hand, a very short password is necessarily weak, because there is only so much entropy you can fit in 5 characters.
This name necklace is made out of Double Thick 0.925 Sterling Silver and hangs on a Sterling Silver Box Chain.
The definition with the average cost is more generic, in that it captures the cases where random choices taken during the password generation process (the one which usually occurs in the head of the human user) are not uniform.
Other popular strength tattoo ideas include the ethnic strength tattoo, the tribal strength tattoo, as well as the word strength written in Hebrew or Arabic languages.

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