The sherut from Tel Aviv to Jerusalem operates on Friday nights but I have no idea whether it runs all night. If I think of it, when I'm passing the sherut stop in Jerusalem tomorrow, I'll ask. There are no other intercity sherut lines to Jerusalem at any time.
I don't know whether there are any other routes that operate throughout the night. I have no personal experience, but I would say it's rather unlikely.
Not a sherut in the strict meaning of the term, but the airport shuttle runs 24/7 and will drop you off anywhere in Jerusalem.
You may be interested to know that in July and August ONLY there are Egged buses on route 480 from north Tel Aviv to Jerusalem (and reverse) hourly until 3 a.m., every night except Friday night/Saturday morning. They are to/from Reading terminal in Tel Aviv and stop at the bus terminal next to Tel Aviv Central/Merkaz railway station, but NOT the central bus station in Tel Aviv. From TA at 12:30, 1:00, 2:00, 3:00, and the same times from Jerusalem.
Apart from that, there are no public transport options to Jerusalem at ungodly times. Hey, do "ungodly" and "Jerusalem" belong in the same sentence? ;)