Password re-use, which is what I believe you are referring to, is generally viewed as a bad idea.
I use the BASE+Differentiator method, and perhaps an explanation of my reasoning will help.
Cryptographically, there is some benefit from using a BASE+Differentiator.
Some implementations (which is to say some Applications, Web Sites, etc.) will use a randomly generated salt that is then added to your password/passphrase. The encryption algorithm then produces a one-way hash of your password. That salt is then stored, in their database, with your encrypted password (the hashed value) in order to be able to compare your password each time you attempt to log in. (The salt is again added to your passphrase, the encryption algorithm is run, and the hashed result is compared with what they have stored in your password field). Thus, if someone were to retrieve your hashed password, that hash value would likely be different from site to site, application to application.
Example would be:
Resultant Hash: hPh7gd6nmpg= <-This is stored as your password
Using the same passphrase, same algorithm (DES3) with a different salt value:
Salt: 456 <-Different Salt
Passphrase: password <-Same passphrase
Resultant Hash: PLhThYNi2FE= <-Different result
There are hashing implementations that do not use a salt, and will produce the same hash value for the same character sequence.
It is important to note that these are one-way Hashing algorithms, so your password cannot be retrieved (easily) from the Hash value. The only purpose it serves is to compare the Hash with a hash generated from the character sequence you typed into the password field. Thus if a site changes algorithms, you will not be able to log in, as your passphrase will generate a different Hash value using a different algorithm, in which case you would have to have your password reset in their system.
Having said that, my reasoning for using a BASE+Differentiator is simple. If someone were to get my plaintext password for Site A (let's say Hotmail), and were to know that I also have a GMail account, or Twitter account, or any number of other accounts (worse... an E-Trade account, etc.), the first thing they will do before trying to perform a computationally expensive brute-force attack, would be to use the password that they already know I use, as it is a reasonable guess that, in an attempt to make life simpler, I re-use passwords.
the BASE+Differentiator method adds a layer of security for the following reason:
If they don't know that I use this method, there is a good chance that they will, at best, lock out any other account that they attempt to use that password on. Being unsuccessful with a known password is enough deterrent, usually, to make them resort to a more time and/or computationally expensive attack vector, like social engineering or brute-forcing it... or even better, abandon it altogether.
Usually, more effort into gaining access to other accounts is motivated by something most of us (normal) people have less of than we think (money, trade-secret information, etc.). In that case (suppose you ARE the one with the formula to Coke-a-Cola), then this added layer of security is enough to slow them down, perhaps long enough for you to realize that someone is attempting to gain access to your information.
To sum up, it is ALWAYS a bad idea to re-use passwords, and knowing that it is difficult to remember a dozen or so passwords (unless you use something like 1Password), BASE+Differentiator is a good, common-sense method.
To make things simple, the Differentiator can be a simple algorithm like:
1. The 2nd letter from the beginning and 2nd letter from the end of the site name
Eg., Hotmail would be BASE+oi
2. The Stock Ticker of the site you are logging into
Eg., Hotmail would be BASE+MSFT (Microsoft)
I hope this is helpful.