While some have criticized the Delta SkyMiles program for its less-than-great mileage options, they do offer some inexpensive domestic award flights that make using this program worthwhile. On top of that, Delta is a member of SkyTeam Alliance, meaning you can redeem your SkyMiles with any SkyTeam Alliance member. These airlines include:

Aerolíneas ArgentinasITA AirwaysAeromexicoKenya AirwaysAir EuropaKLMAir FranceKorea AirChina AirlinesMiddle East AirlinesChina EasternSaudiaCzech AirlinesTAROMDelta Air LinesVietnam AirlinesGaruda IndonesiaXiamenAir

Unfortunately, Delta was one of the first airlines to get rid of its public award chart and change to a dynamic pricing system for award flights.

Delta has put many routes between the US and Mexico/Caribbean on "sale" right now through September 5, 2018 (this coming Wednesday). I say "sale" because Delta doesn't have a published award chart anymore, but we know from charts maintained by people like us online that the standard lowest level US > Mexico and US > Caribbean award price is 17,500 Delta miles one way.

Through August 16, 2017 (tomorrow) at 11:59 PM ET, you can book roundtrips between the United States and Tokyo, Seoul, and Beijing in Delta's new Premium Select Cabin for 80k Delta miles roundtrip, or 65k roundtrip in economy.

Through July 12, 2017 (tomorrow) at 11:59 PM ET, you can book roundtrips within the United States (on select routes) for travel September 6 through October 31, 2017 for only 20,000 Delta miles.
Sale Routes
Delta states that the sale applies to award flights with the following origins/destinations:

Washington, DC
Jackson, WY
Bozeman, MT
Idaho Falls, ID
Reno, NV
Phoenix, AZ
Knoxville, TN
Philadelphia, PA
Boston, MA
Salt Lake City, UT
Rapid City, SD
Las Vegas, NV
St. Louis, MS
San Antonio, TX
Buffalo, NY
Sacramento, CA

Flights don't need to be direct.

Through March 15, 2017 (this Wednesday) at 11:59 PM ET, you can book roundtrips to Europe in Delta One for travel August through October for only 110,000 Delta miles. The standard price is 140,000 miles roundtrip.

This isn't a particularly earth shattering award price to Europe in a flat bed. You can fly United or American's Business Class for almost the same price any time you can find award space (price is 57,500 United miles or 57,500 American miles respectively).