The idea is admirable, but it's a really bad alternative to having unique, random passwords for each site. With this, it's trivial to recover all other passwords if you know just one of them.
If it gives you 'aJ2Y64f' and 'lLv8PV2S' and you decide to make those 'aJ2Y64fa' and 'lLv8PV2Sl' all of a sudden the ability to work backwards is lost, no?
The best solution is randomness -- that's why secure random number generators are so fundamentally important in cryptography.
This:
'facebook' + 'mypassword'
'twitter' + 'mypassword'
'foursquare' + 'mypassword'
Password manager with unique passwords: 'mSX32ZyKZXptY3E'
'33RiKbc3n6sA6IY'
'4kGzFtWDd0rnti6'
All I have to do is figure out what you named the site that I compromised, then do exactly what I'd usually do to recover your password, and, voila, I can now access all sites you use it for. Compare this to the password manager example where each password has been generated at random--one password communicates no information whatsoever about the other.