Nylok Nut vs Plain Nut

You won't need a locking/star/crinkle washer, but you may still want a plain washer depending on the application to spread the load, protect surfaces give even tightening etc
Del

There is strong data that lockwashers do not in fact prevent fastener loosening. Nylock washers do. flat washers don't play a role on fastener loosening but they do prevent substrate damage and tend to spread the clamping loads for softer materials.

excuse me i meant nylock nuts, not washers. mea culpa.

Don't forget about the increased level of prevailing torque when tightening fastener sets that include Nylok washers!

Just like anything else, it depends on the application. Not to beat a dead horse but the washer can distribute load, especially over (relatively) uneven/rough surfaces. If you would like to control the pretension of the fastener/joint beyond the level of "by feel", you might still want a washer.

Also, although star washers and other "bite" type of locking mechanisms have been shown to not be significantly effective, many engineering firms and organization subscribe to the "belt and suspenders" methodology. Just food for thought.