Redmine

You can use users custom fields for that.
Go to 'Admin -> Custom fields -> Users' and create a new
field.

A quick example (I've just added the phone number),
http://demo.redmine.org/account/show/3

There's a restriction with this solution: the user can't update
this information himself.
I could add a flag on users custom fields to specify if the field
can be updated by the user himself.

Great, I didn't realize custom fields could be added to users
- excellent :-)