What would you recommend instead? If you insist people remember all of their passwords in their head, you'll end up with them using the same password for everything.
I like the idea of hashing off a root word + site. I'd rather have the browser do it for me though, and I don't think there's anything on the page itself that I could depend on to hash with. Maybe the domain?
To be honest, firefox has an encrypted database of site-passwords. What's wrong with that?
I have a system like that, that takes a master and the domain. The advantages over the Firefox password manager is availability and not having to worry about backups. Since I know the algorithm, I can recreate any password using widely available tools.
For example, if you're password is "puppy" and you're signing-up for HN, your password would be:
pHuApCpKy
And, if you wanted to make it stronger, salt it with some special characters.
p~Hu!Ap@Cp#Ky$
... which is just the shift-characters on a number row in order.
This way, you only have to remember one password, and it is service specific, and pretty strong. No password manager needed.
Of course, I don't do this. I use a 1Password and KeepassX.