SQL - When would an empty OVER clause be used?

OVER() is part of analytic function and define partitions in your recordset. OVER() is just one partition and applied to the whole dataset

i.e. COUNT(*) OVER() will return in each row how many records in your dataset.

look to this http://msdn.microsoft.com/en-us/library/ms189461.aspx

Say our table is employees:

+-----------+-------+---------+
| badge_num | name  | surname |
+-----------+-------+---------+
|         1 | John  | Smith   |
|         2 | Mark  | Pence   |
|         3 | Steve | Smith   |
|         4 | Bob   | Smith   |
+-----------+-------+---------+

Running

SELECT surname, COUNT(*)
FROM employees
GROUP BY surname;

we'll get:

+---------+----------+
| surname | COUNT(*) |
+---------+----------+
| Smith   |        3 |
| Pence   |        1 |
+---------+----------+

While running

SELECT surname, COUNT(*) OVER()
FROM employees
GROUP BY surname;

we'll get:

+---------+-----------------+
| surname | COUNT(*) OVER() |
+---------+-----------------+
| Smith   |               2 |
| Pence   |               2 |
+---------+-----------------+

In the second case, in each row we are just counting the number of rows of the whole select (not the single partition).