Which aircraft maintenance repairs require a test flight?
I've been in aircraft maintenance for over 15 years, and have worked about 10 different types of narrow and wide body aircraft, and have never once seen a maintenance manual direct me to test fly an aircraft. 

There is a reason for this, though. Repairs done during routine maintenance are designed by the manufacturer such that the repair itself makes the aircraft airworthy. That is usually part of the manufacturing and STC process, if I'm not mistaken. 

That being said, it's not entirely uncommon to have maintenance control or even maintenance management request a test flight. Usually this is done for troubleshooting or for repair verification. This is largely due to the fact that there are some problems that maintenance cannot duplicate on the ground. For example, I recently worked an airplane whose window heat failed at the top of descent about once every ten or eleven flights. I can simulate a lot of things on the ground, but what I can't simulate is the actual descent of the aircraft at about 37,000 feet! The problem had been ongoing for four or five months, but was sporadic enough not to trigger any alarms in the analysts office. It was only when you paid careful attention to the history of the problem that you realized it had major issues.

Due to regulatory requirements, and the way our GMM is written, if the aircraft had another occurrence on the next flight, it'd be "dead" at the next station it landed with no MEL relief. We made a repair, but it was really only a guess because there were no actual signs of wear/fatigue/damage and everything tested normally. Management requested a test flight, and asked the test crew to run it through the wringer, to see if it would fail. 

On the other hand, there are certain systems that may require flight crew verification during flight prior to recertification. An auto land system that has had chronic failures may require the flight crew to perform an automatic landing before it can be recertified back to full CAT III landing status. But, this can often be done on a revenue flight, and is often not a dedicated flight meant to specifically test the system. 

There is also the rare case in which major structural repairs may require a test flight. I once saw a wide body aircraft that had a tail strike on landing. The damage was so severe, it literally twisted part of the empennage. In order to be repaired, our company required major involvement from the aircraft manufacturer. The manufacturer did provide a repair, but for obvious reasons, the engineers actually mandated several test flights afterward. 

However, as far as I know, there is no regulatory requirement which says that a certain repair requires a test flight. From what I've seen, and perhaps this may sound awful, you kind of "know" when an airplane needs a test flight.