While you cannot transfer your Delta SkyMiles to other airlines, you can use your SkyMiles to purchase award flights on SkyTeam alliance airlines that partner with Delta.
There are over 2 dozen partner airlines with which you can book using your SkyMiles. The majority of partners can be booked online at Delta.com but a few you must call Delta to book using SkyMiles.
Also, it is worth noting that Delta SkyMiles never expire.