I know most people just want to go somewhere and come back with their miles, but I am biased toward BIG trips. For the most part, the best way to book such big trips is as a series of one way awards with many different types of miles, taking advantage of the sweet spots with each program.

All Nippon Airways (ANA) has reduced fuel surcharges drastically on awards that travel to or from Japan. Now you can fly to Tokyo from the United States for 75,000 miles in flat bed Business Class roundtrip plus low taxes plus a $4--yes four dollar--fuel surcharge. That's tens of thousands of miles fewer than competitors charge.

The above screenshot is of a roundtrip Business Class award flying ANA between Los Angeles and Tokyo in February 2017.
Routing Rules
ANA has two award charts.

Last week my friend flew 24 hours of Lufthansa First Class and had a 3.5 hour layover in the famous Lufthansa First Class Terminal, which he booked for 125,000 United miles and $58.

Elite members of United’s MileagePlus frequent flyer program get access to extra Saver award seats in economy class. (Platinum and higher members also get extra business and first class seat availability.)

United credit card holders also get the extra Saver economy award space set aside for elites. That includes people with the United Explorer, Business Explorer, and Club cards.

I consider this one of the biggest benefits of the cards, and, oddly, it is a benefit that is completely unadvertised and possibly unintentional.
Recent Example
I have the United Business Explorer card and no elite status with United.

Update: I used this trick successfully. Here was my experience.

As I led a session at the Chicago Seminars this weekend on "Special Awards," someone chimed in with an intriguing tip:

There is a simple method to avoid the $75 "close in ticketing fee" on United awards that is triggered when you try to book a ticket within 21 days of departure.

I tested out the proposed method yesterday, and I have some input on how it works.

It is cheaper to book the exact same United flights to Hawaii with Singapore KrisFlyer miles than with United miles.

United charges 22,500 miles each way in economy and 40,000 miles in First Class between the mainland and Hawaii
Singapore charges 17,500 miles each way in economy and 30,000 miles each way in First Class between the mainland and Hawaii

That's a humongous difference. Instead of costing 90,000 United miles to get two people from your home airport to Hawaii and back, you could pay 70,000 Singapore miles.

Update 4/13/16: Expert Mode was down for weeks, but now it is up and working again.

Turkish Business Class award space is widely available from this summer through the beginning of next year to Europe.

United.com is the fastest way to search most Star Alliance award space. I frequently use the search engine even if I'm using another type of Star Alliance miles.

I often use the site's calendar to search two months of award space at a time on a single route.

On roundtrip United awards, you get one free stopover in addition to your destination and up to two open jaws.