| You should put a finish on the neck. It's not really needed on the rosewood, ebony or other oily wood fingerboards. But the back of the neck where your greasy, sweaty hand slide around while you're playing, plus humidity in the air can soak into unprotected wood and cause warping of the neck and staining of the wood.
Real tung oil (if you can find it easily) is sometimes used and I consider it a bare minimum finish as it doesn't waterproof the neck as well as some other finishes. The so called Danish or Scandanavian or Swedish oil finishes sold usually don't have much tung oil in them, if any and are actually varnish/oil mixtures designed to soak into the wood like tung oil does and give a similar appearance and feel with more protection. There are a number of good brands that work from MinWax, Deft, and others.
I like to do a sealer coat with the MinWax oil and then coat with a couple coats of wipe on varnish like MinWax wipe on polyuretane. This dries pretty slick so after it's hardened for a couple days I rub it out with steel wool or a ScotchBrite pad to give it a smoother feeling satin finish that doesn't make your hands stick. | 
