User Module modifications I need to add about 64 custom fields to the user object. These fields will be filled when the user is created and updated from a 3rd-party database when the user logs in.

How would I go about making these modifications? Would I subclass the user or just make a new module to do this?
Clive's answer is right for Drupal 6.

For Drupal 7, you'd implement a Field. This field would provide the 64-field form to fill out, the way to display the info, and know how to query the external database. (Obviously there's some room for design improvement here.. I'm chunking all the different pieces into one meta-field, but you could split it out however you want.)

Then you go to admin/config/people/accounts/fields and add your field to the user account profile. When you add it, there will be an initial configuration page for that field instance, and you'd check 'Display on user registration form.'

Easy as pie, right? :-)

There's a generic field implementation example in the Examples project.