I'm storing some passwords in a database using PHP+MySQL
I realise that MD5 is not a secure method to store passwords, but for now I'm using it mainly to ensure that regardless of the length of the password, it can be stored in the database easily.
For that I'm hashing the password using PHP and storing it in the database.
Is there any practical limit on the length of a password I can store using this manner?
(security is not of importance here, I am using the hashing only for convenience)
No, you do not have to limit the length. PHP already contains some safety checks on the maximum request size to avoid malicious users from filling up your memory.
But as you mentioned: MD5 is NOT ACCEPTABLE to hash passwords. Neither is any other hashing algorithm unless you use it with a salt!