United has announced a 15% to 25% discount on economy class awards from the US to Europe:

Roundtrip awards booked between now and December 8, 2015
for flights flown between January 11 and March 10, 2016
on itineraries wholly operated by United and United Express flights
will cost only 45k to 51k miles roundtrip, depending on the days of travel

United has run a nearly identical promotion for the last several years, so maybe this is becoming a yearly occurrence.
United’s Current Promotion

I did a few dummy bookings to test out what’s possible.

Right now, Air New Zealand has a monopoly on direct flights between the United States and New Zealand with flights between Auckland and Los Angeles, San Francisco, and Honolulu. It adds an Auckland to Houston flight on December 15, 2015.

The good thing about booking Air New Zealand award space is that you have access to the whole country through connections instead of just Auckland.

In January, I'll be in the United States, and I'll need to get back down to Southern South America.

In January, I'll be in the United States, and I'll need to get back down to Southern South America.

Through December 14, 2015, United is offering up to an 85% bonus on purchased miles. The maximum bonus is targeted with some people being offered 60% and 70% bonuses. Also the size of the bonus depends on the number of miles you buy, with the largest 60%, 70%, or 85% bonus kicking in at 40,000 miles purchased.

Log into your account here to see the bonus you are offered. I was offered the 85% bonus.

United miles normally cost 3.5 cents per mile plus a 7.5% tax, bringing the full price to 3.76 cents each.

United now shows its award routing rules online. (Dummy) book an award, and on the page where you review your complete award itinerary, click "View fare rules and restrictions."

You will get a very long list of the award rules that pertain to your award ticket.

United now shows its award routing rules online. (Dummy) book an award, and on the page where you review your complete award itinerary, click "View fare rules and restrictions."

You will get a very long list of the award rules that pertain to your award ticket.

How many miles would it cost to book a United award in economy from Aruba to Panama City to Bogota to the Galapagos with stops for as long as you'd like in each place? 

There is a layover in Quito, but that doesn't affect the price. For reference, this single award would look something like this:

This award costs only 20,000 United miles.

Turkish Business Class flat bed award space is wide open to Europe, Africa, the Middle East, and Indian Subcontinent for Summer 2016. You can book award space for 2-8 people in Business Class on routes from America to Turkey and beyond with United miles, LifeMiles, Aeroplan miles, Asiana miles, and many other Star Alliance miles.
Where Turkish Flies
Turkish will soon fly from nine American cities to Istanbul.

From Istanbul, you can connect to over 100 countries.