"123456" and "password" as crack standards I know that when we encrypt, we use standard encryption technologies and to store data it's often stored as a hash.

By encrypting a common password, for example 


  "password"


using MadeUpHashingTechnology it will always equate to  


  "awregk;4"


this becomes a standard to use in identifying my hash. Now crackers can look at MadeUpHashingTechnology-Dictionary.com for the most common hashes and see my data more easily.

If I identified n-common or low-strength passwords and simply left them unencrypted (or used a distinctly different encryption) would that help in reducing dictionary attacks? (I'm assuming my password database has been compromised in this scenario)

Would the database need to be compromised for a dictionary attack to be useful?
Using several different encryption algorithms, and not disclosing which is used in each particular case would require password verification to try all possible algorithms. Feasible only when using just a few algorithms. 
Truecrypt does this, for example.

This could strengthen security, when implemented properly - but it is much more difficult to implement.

Proper solution - salt.


Do not use MadeUpHashingTechnology without salt.
Do not use  MadeUpHashingTechnology ever, use public, verified crypto.