This is a topic I'm pretty wrapped up in, as I prefer to only own lenses with some of those "special" qualities. Every system has different candidates, but I learned a long time ago that if you own the non-special lenses you either regret using them when something big happens, or you just leave them on the shelf and pack the others that you love a bit more.
This is a huge part of what drew me to Fuji.
Here's my read of the Fuji line, from that perspective and from my own pretty rigorous research. These are the lenses that I feel possess "special" qualities of one sort or another.
1. The 35 1.4 is a superb lens. My big drawback with it was that the bokeh could take on a nervous quality in some occasions where high contrast light and high contrast backgrounds merged in the background. But the images from it can be amazing. But it had a pattern that I see in many Fuji lenses where they have good contrast, and defined boundaries between tones, and yet certain tones soften and create very smooth transitions. And yet, the edges stay distinct. Generally, it seems that skin tones (and similar values) are much smoother, whereas the darker tones have firmer boundaries. This makes soft light creamier. I love the effect, and it's similar to what drew me to Leica lenses back when I was learning and learned with a Leica film bag. Fuji and Leica handle these "creamy/contrasty" tradeoffs differently. They're not the same. But it's the same qualities beneath the surface between them, and I personally believe that Fuji shooters are getting some exceptionally brilliant lenses for their system. It's kind of a golden era, but as with most eras, people won't know it until it has passed and they miss what they had.
I will say that a hidden value in that 35 1.4 is it's ability to shoot landscapes. I like taking moody black and white Landscapes (primarily centered in the American West). These aren't four exposure landscapes, digitally knitted together over 3 days of post processing. Amazing work that some do with those. But I'm more interested in the gritty, moody images like Robert Frank would have looked for. And that 35mm lens had a unique ability to have the sky and the highlights softly texured, but keep some firmer boundaries to the darker details (leaves, horizon outlines, and etc).
2. That said, I find that the 35 f2 actually possesses it's own unique qualities--along the same lines as described above, but expressed in very different ways--and I like these qualities even better than I liked the 1.4. The bokeh on the f2 is smoother, and it's a good mix to go with the creamy skin tones and highlights. It's not that the f2 is "better" than the 1.4. It's just different, but different in some very interesting ways. There's just a dreamy kind of quality to them that I can't get, in the same way, from other lenses.
3. The other lens I've found that has this same dynamic--but again, expressed in different ways--is the xf56mm. This might be the greatest workhorse lens in the whole lineup. And in fact, I find it adds smoothness to a huge range of skin tones, from dark to pale. But where it also surprises is in how it can shoot moody landscapes in the same vein as the 50mm. How it chooses to separate smooth tones from darker edges is just... special.
4. Another "special" lens is the 23 1.4. This lens has less of the creamy/contrasty qualities of the 35s and the 56, but it it does some other things better. The out of focus areas in the background are soft, the main subjects are pleasantly sharp even at wide apertures, and you can fit more context into the frame in a pleasant way. Something about how the lens allows light and sharpness to focus on the main subject, but then begins receding the background both in sharpness and in tone is pretty unique. I shoot most weddings with this lens on one body, and the 56 on the other. When soft light floods a frame, with this lens, you can get some of those very soft tonal transitions as you see with the 35s. The difference is that it takes a LOT of light do get the effect with the 23, whereas teh 35s seem to do it in even low light.