A current date default might be useful to record:

The current timestamp is similar to the current date default, but offers greater accuracy. For example, a user of a contact management application may have several interactions with a single customer in one day: the current timestamp default would be useful to distinguish these contacts.

Since it records a date and the time down to a precision of millionths of a second, you may also find the current timestamp useful when the sequence of events is important in a database.

The default timestamp provides a way of indicating when each row in the table was last modified. When a column is declared with DEFAULT TIMESTAMP, a default value is provided for inserts, and the value is updated with the current date and time whenever the row is updated. To provide a default value on insert, but not update the column whenever the row is updated, use DEFAULT CURRENT TIMESTAMP instead of DEFAULT TIMESTAMP. See the DEFAULT clause in CREATE TABLE statement.

For more information about timestamps, times, and dates, see SQL data types.