I don't listen to huge amounts of Nu Metal. Nowadays the only genuinely Nu Metal bands I really listen to off the top of my head are Korn, Slipknot, Dry Kill Logic, (hed) p.e. and Ill Nino. I adore Deftones as well, but don't really consider them Nu Metal (save for Adrenaline). I listen to Metal and Rap so, if it's done well, Nu Metal can be pretty enjoyable for me. I like heavy, aggressive music in general, and so whilst I do like Death Metal, Black Metal etc., sometimes I want something that will deliver more direct and simple aggressive grooves. Bands that don't make me think much or require that I absorb and study the music; just music I can bob my head to after a few beers.
I'll second the comment that Rage Against The Machine, whilst including elements of Funk and Hip Hop, aren't really part of Nu Metal as it is known today. They, along with Faith No More, simply laid the foundations for the genre.
As for whether Nu Metal should be classified as a Metal genre, I think my general answer would be "yes", but it does depend on the band. Papa Roach and Linkin Park have both adhered to the Nu Metal conventions, but are so commercial and watered-down that the "Metal" part of the sound is scarcely there. Korn have released music I would consider Metal in the past, but their forays into Industrial, Funk, Hip Hop and latterly Dubstep mean that I don't call them a Metal band; just a band that has played Metal. In other words, I believe that a Nu Metal band can be considered Metal, provided that Metal plays the biggest role in the music. Slipknot, Otep and bands liked that come to mind. Whereas, bands that don't place emphasis on heaviness or other "Metal traits" like Linkin Park are not, and never have been, Metal in any way, shape or form.
Hope this makes sense.