1. be long enough (e.g. 8 characters or more)
2. not be in the list of 10k most used passwords
3. not simply reuse words present in the username, email, birthday (if my application knows about it)
This keeps it open and only interferes with truly stupid (aka insecure) password choices.
Additionally I like to propose 8 passphrases to the user so they can choose one of their liking with one click (this also serves as a proposal what a good passphrase could look like).