Presented as Q&A format (Originally posted by Alex_B)

Q: What is a stopover?
A: A stopover on an international itinerary is any break in your air travel for more than 24 hours except at the destination.

Q: What is an open-jaw (OJ)?
A: An open-jaw is where you travel by your own means (either land, sea or a separate air ticket) between two points in a journey.

Q: How many stopovers am I allowed on a roundtrip award?
A: One stopover is permitted.

Q: How many open-jaws are allowed on a roundtrip award?
A: Two open-jaws are permitted.

Q: Can I have a stopover or open-jaw on a one-way award?
A: No

Q: Can I have a open-jaw at both the stopover and destination?
A: It has become extremely difficult to book an open-jaw at the stopover. Best not to count on getting one.

Q: When I try to book my OJ itinerary online, the website errors out. Does that mean there is something wrong with my itinerary?

A: Not necessarily. The website typically can't handle complex itineraries. These must generally be called in.

Q: Can I transit my destination multiple times (e.g. fly to JNB, fly to CPT and then return home via JNB)?
A: Yes, plenty of posters have reported success in booking this. You can only stop in your destination for > 24 hours once though.

Q: Can I cross both oceans?
A: No.

Q: Is EWR-PVG transatlantic or transpacific?
A: US-East Asia/South East Asia is always transpacific no matter what geography might suggest.

Q: Do I pay more for a stopover or open-jaw?
A: Typically no additional mileage is required but additional taxes or fees are often payable (especially in UK with high Air Passenger Duty). Extra mileage will often be required if an open-jaw or stopover adds a higher cost region into the itinerary. Also awards wholly within CONUS, Canada and Alaska (formerly known as Series 0 awards) require additional mileage (10K miles) for a stopover of >4 hrs.

Q: What's this about a "free one-way" I can get on a UA award?
A: The term "free one-way" is a misnomer and often confuses people (and may annoy the regulars here!). The technical definition of this concept is "stopover at origin." There have been mixed reports recently about UA's willingness to ticket a stopover at origin.

Important Notes - PLEASE READ:

1. Stopovers and open-jaws are NOT additive. You do not get extra stops included in your itinerary simply by making an open-jaw out of it. This is probably the number one error made in attempting to construct a complex itinerary. If you have more than two stops >24 hours on a roundtrip award, it is not legal and will not ticket.

2. An open jaw always creates a stopover, even if you're stopping for less than 24 hours.

3. Many awards are subject to segment or "transfer" limitations. For example, the North America to South Asia award is currently restricted to four transfers in each direction.

Seeing your fare construction on an already booked award ticket:
In order to see your award fare construction to see where your stopovers and destination are, follow these steps.

Go to http://www.saudiairlines.com/

Then hit "Manage My Bookings" and select "E-Ticket"
Enter your UA ticket number (hint: 016 will go in the first box, and then everything else in the second box). Then your last name and hit "Retrieve My Booking". On the next page you'll see a line like this under "Fare Calculation":

CHI LH X/FRA LH ROM0.00CSM/YB52 /- FLR LH X/FRA LH X/DUS LH CHI UA SEA

This example is:
ORD-FRA-FCO
Open Jaw at Destination
FLR-FRA-DUS-ORD
Stopover at origin
ORD-SEA

Previous thread on this topic:

Rules for Open Jaw & Stopover Award Flights (Consolidated)

Consolidated: Rules for Open Jaw & Stopover Award Flights [2014]