I hear that if you want to fly somewhere, you can get really cheap
tickets at the last minute before they depart if they need to fill up
empty seats.  I looked all over the internet to try to get information
about this, but all the websites claiming to have last minute deals
didn't have actual last minute deals.  I mean, suppose it's
Thursday night, I'm in Philly, and I'd be willing to go down to Philly
airport at a moment's notice any time that night or in the next
morning and catch a flight to Boston.  Would I be able to get any
super cheap tickets for any flights to Boston that aren't sold out
where they just want to fill up some seats?  If so, how would I go about
getting these super cheap tickets?

As you have probably discovered, those very cheap "last minute"
flights include a vacation package.  That is why they are so cheap,
because the travel operator is willing in the last minute to take very
little to fill empty seats and rooms that he has contracted to pay
for.

Cheap individual flights are offered by airlines to people willing to
book in advance, usually with no option to chance or cancel.  Makes
good advertising.
If they offered empty seats at cheap prices in the last minute,
everyone would wait to book.  The airlines reckon that anyone having
to fly in the last minute will have a strong enough reason that he
will pay full fare.

I expect that they know their business.

Myoarin

I believe your best bet is www.site59.com, where they only allow you
to book a flight between 3 hours and 14 days from departure.  You must
purchase the flight as a package with hotel or rental car, but the
prices are indeed extremely low.

Here are a few sites you might try: 

http://www.lastminutetravel.com/PageFlightSearch.aspx
http://www.hotfares.com/last-minute-travel.php 
http://www.airtkt.com/cheapestlastminutetravel.asp 

For more, just try searching on [last minute airfare]

Good luck,
Byrd-ga