Let's begin with a very ancient set: Crabs and Gold Fish Set by Ichikawaya. My Japanese is close to non-existent but Google Translate tells me it's a reproduction of an antique set. The pinzu in this set are crabs while the souzu are gold fish. Sure, green souzu isn't green, but everything about this set says it's from a prior era and high class.
The Tengen Set by Ichikawaya is currently the set I'm thinking of buying in the near future. It has a classy look that doesn't feel old. EDIT: Well now it's sold out. T_T
One of most changed sets I'm eyeing from time to time is the Galaxy Set by Ichikawaya. It doesn't look like any other Mahjong Set I've ever seen. In this set, Pinzu are planets, manzu have the man symbol replaced by planet symbols, and souzu are all star constellations. To stay in the theme, red fives are replaced by blue fives. The winds are just simple letters, E S W and N. The dragons are the western zodiac signs divided into 3 groups of the same colour. Flowers and seasons are more symbols that are used in Astrology. It's such different take on tiles, I'd consider it more a collectable than an actual set to play.
Of course, there's the Doman Mahjong Set from Final Fanatsy XIV. Pinpu in this set are Namazu, souzu are Sabotender, and the manzu are with stylized arabic numbers. The only problem is some of those numbers also look like Katakana and might throw you for a loop. (Damn you, Kupti Koop!) If not for the ongoing pandemic, this set is widely available, so I decided to make this my go-to set for teaching mahjong to people that just want to get an initial look at it.
EDIT 2022-06-02: The set was removed from SquareEnix's US Store, not that it really matters, it was constant unavailable anyway.
Stepping away from Riichi tiles, I recently found the MACHILL Set by THE 90s LAB. It's very modern and simplistic. The only thing I don't like about it is it has white back. Anyway, I can't find it anywhere, so even if I would want to buy it, I currently can't.
Finally, I just found a minimalistic set from the west, The Minimal Line by The Mahjong Line. I would very much like to link that set, but there was some outrage about alleged “gentrification of Mahjong”. So Asians can do whatever they want and it's a unique Mahjong set, but when 3 White women do it, it's called gentrification?! As one would expect of the internet outcry machine in the early 20s, some hacked the site and wiped it. It's quite a bummer, I like the look of the Minimal Line. 400 bucks might have been too steep of price for me. But I can still admire its looks. The set looks nice, but if I have to nitpick, the flowers and seasons aren't numbered and not easily divided in sets. But that's only problem if you actually plan to use this to play a variant that needs those with numbers and in two sets. It's most likely the creators only intended this for American Mahjong. Yes, American Mahjong, it exists. In fact, it has existed for so long it has diverted a lot from Chinese Mahjong, which apparently is centuries old, at least, according to most news sites are FOMO'ing in on the outrage. The oldest record of its existence are from the late 19th century, 1870 to 1890, I believe that's way too young to be called “centuries” old. By the way, American Mahjong was created in the 1920s.
So I'd like to give the creators constructive input to consider that in their next design.
Oh wait, the outrage machine made them shut down… this is why we can't have nice things. EDIT: The site wasn't purged intentionally by the owners, so I can even link to their product!
This was to be the end of my little list, but meanwhile the camp that actually enjoys nice things pointed me to another Riichi Set: ah, Asia and their love of puns! The Big Sushi Set by Taiyo Chemicals replaces all the common elements with rice, fish and seaweed.