Here is a list of what I believe to be truly rare items in destiny. Please add others that you believe are truly rare, note this isn't about the BEST, it's about the rarest in terms of drop rate and number of opportunities per week to possibly get it.
1) Faction Shaders (ex. Revenant, Amalthea, Babylon shaders)
2) Faction Ships (1 available from each faction).
3) Faction Weapons only obtainable from packages, nightfall, or engrams. (Ex. Red Hand IX, The Conduit, Final Rest II).
4) Praetorian Foil. From hard VoG oracles. It simply has the lowest drop rate compared to other items in the vault of glass including the vex mythoclast.
5) Hardlight (RNG only) Xur has not sold this weapon.
6) Thunderlord (RNG only) Xur has not sold this weapon.
7) Gjhallarhorn (RNG or purchases from Xur during Week 2).
8) Necrochasm (lots of luck required in terms of RNG).
9) Substance 321 Shader
10) Arctic Proxy Shader
Let's hear some others. Don't say exotic pieces that have been sold multiple times by Xur.
Edit: Not in any particular order.
Edit: New Additions:
11) Queens Wrath Shaders, class items, and weapons. For example prism dancer, rose gold, The supremacy, etc.
12) Praedyth's timepiece and Fatebringer seem to be candidates, my question, do you typically see at least one drop for somebody per raid?
13) I'm not on play station but I believe hawkmoon and Monte Carlo are other rare exotics that haven't been sold by Xur. Note fate of all fools isn't obtained via normal drops so I am not going to add that.
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Carthage shader