"My point isn't that strong passwords aren't important, it's that if the salt + hash procedure that was used is adequate, then the strength of any individual password becomes insignificant in relation to the strength of the password + salt."
I'm pretty sure that's not true any more. Modern gpu based password crackers like Hashcat will rip through their lists and algorithmic modification of those lists just as quickly with no salt, 2 byte salts, or 16 byte salts. The salt adds no protection at all against a brute force attack - especially wordlist-based brute-forcing (at least not against an individual password - it _does_ mean that the first time you find one account using "password123" you don't automatically have all of them).
This article: http://arstechnica.com/security/2013/05/how-crackers-make-mi... explains it nicely - it kind of muddies the water by concentrating on a list of plain MD5 password hashes, but Hashcat is just as happy to rip through any of over 30 different password algorithms including just about any variant of MD5+salt and SHA256+salt (http://hashcat.net/oclhashcat-plus/#features-algos). (Astute observers will note that list _doesn't_ contain "slow hashes" like bcrypt/scrypt/PBKDF2 - that's why Coda's "just use bcrypt" is still good advice for developers storing passwords.)
The only sensible password advice these days is:
1) Where possible, use two factor auth - make sure the email account that receives password resets is tfa secured, or all your passwords can fall to an attack on that email account.
2) Always use password storage/generation software (1Password/KeyPass/LastPass/whatever), and use a long but memorable passphrase for it.
Once you've chosen to do that, it them becomes easy to follow the next rules:
3) Never reuse passwords - generate a new random unique password for every login.
4) Use long complex passwords - at least 15 characters including upper/lower/digits/symbols. (I use 25chars except to the few passwords I need to type manually regularly - 1Password can't autofill my AppleID password on my phone or iPad - so I've got a 15char password in my head for that).
5) Recognise that some passwords are more important than others - your online banking, PayPal/eBay, Amazon, AppleID and/or Google Account are the obvious ones, but also take extra care with domain registrar accounts - if I can change your DNS, I can update your MX record, and bam! I've got your password reset emails. For the same reason your dns hosting is a critical account, if I can update the MX record on your webhosting cpanel account or your linode/rackspace/whoever server - I can get all your password reset emails. Treat all these passwords with extra caution - don't type them into "untrusted" computers.