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?
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, in addition to the destination, is permitted (an unlimited number of stops less than 24hours is allowable).

Q: How many open-jaws are allowed on a roundtrip award?
A: Two open-jaws are permitted. These must be at the stopover, destination or origin.

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: Yes, plenty of posters have reported success in booking this

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: Yes. The rule that prohibited crossing both oceans appears to have been removed from both MP and *A award rules. There are many many successful examples of people booking these itineraries.

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 awards?
A: The concept of free one-ways is a misnomer and often confuses people, it is better to consider it a stopover in the city of origin. If you have a simple roundtrip award without a stopover, you can often create a stopover and open-jaw at your origin on the return leg to add an addition flight. E.g. I wish to book EWR-LHR (destination)-EWR which is a roundtrip US-Europe award. I could also book this as EWR-LHR (destination)-EWR (stopover)-SFO for the same mileage (and a few dollars of extra tax). The EWR segment would need to be within 330 days of booking and would be subject to the usual change fees.

Other notes:

• The open-jaw portion must be smaller (in miles) than any other leg. -While technically true for revenue fare construction this is not strictly enforced on awards.
• For awards between CONUS/Canada/Alaska and South Asia award regions the maximum number of segments is 5 segments each way on a round-trip and 4 segments on a one-way. (Note that many FTers report recently being read a memo that imposes an eight segment maximum on a roundtrip (4 each way). It is unclear whether this eight-segment maximum is limited to South Asia routings through Europe or North Asia, or has broader application.)
• 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.

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