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.

Last month I flew from Houston to Honolulu in United First Class. I had booked the award with 30,000 Singapore miles because Singapore miles have access to the same Saver award space on United flights as United miles do, but Singapore charges fewer miles.

Update 2/12/16: United brought back the nonstop calendar. The single column for Saver and Standard economy space remains.

I covered two months ago why the new united.com stinks for award searching. My biggest complaint is that even if you specify a "nonstop only" search, the search calendar does not show you nonstop only results.

I used to be able to see space on a route for two months at a time on united.com, now I can see it one day a time.

I booked myself an award from Honolulu to Manila with eight take offs and landings and multi-day stops on Pohnpei and Palau for 47,500 United miles by taking advantage of the free stopover on roundtrip United awards and how lenient the definition of "roundtrip" is.

A few weeks ago I shared how you can book United's amazing Island Hopper route with miles and stopover at one of the otherwise-nearly-impossible-to-reach islands along the way.

The Island Hopper.

Through October 23, 2015, United is offering up to a 80% bonus on purchased miles. The size of the bonus depends on the number of miles you buy, with the largest 80% bonus kicking in at 30,000 miles purchased (54,000 total miles after the 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 is offering a 20% discount on roundtrip Saver economy awards booked to Hawaii by November 5, 2015 and flown October 19, 2015 to March 3, 2016. The total cost of a roundtrip is 36,000 miles during the sale. There are blackout dates from November 20, 2015 to December 3, 2015 and December 16, 2015, to January 5, 2016.

Don’t Book This Promotion
If you have United miles, this may be a good deal. If you have Ultimate Rewards, do not transfer them to United miles to book this deal.

To anyone who will listen, I say that you should not expect to use your miles at peak times on high demand routes. Airlines use miles to get rid of distressed inventory--seats they don't expect to sell.

United operates a route from Honolulu to Guam with five stops twice per week on Mondays and Fridays.

Through September 30, 2015, United is offering up to a 75% bonus on purchased miles. The size of the bonus depends on the number of miles you buy, with the largest 75% bonus kicking in at 40,000 miles purchased (70,000 total miles after the bonus.)

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