I’m not sure there are must haves, but I enjoy:
Dawn of the Zeds 3rd edition: Lots of content and semi complex rules. On the heavier side.
Eldritch Horror: Much better solo than with people. I play with 3 or 4 investigators.
Spirit Island: Still learning. I like the simplicity of the design, and the theming is so good it avoids it becoming dry.
Unicornus Knights: as said above.
I also, really, really like:
Enemy Action: Ardennes: I play mostly German Solitaire, and only the short game (I don’t have a table to leave the long game set up for the aprox. 30 hours the full campaign can take.
Conflict of Heroes + Solo Expansion
BUT: these last two are wargames and to be approached with caution. EA: Ardennes has like 60 pages of dense (well written, but dense) rules. And Conflict of Heroes is a light weight wargame (so heavier than a heavy euro), on top of which you have to put the solo system.
However, as opposed to the previously mentioned games, in these you get the feeling you are playing against an opponent at the same decision and power level as you, not just against a semi random pressure system like all the previous games. Also, they don’t use the usual flowchart bot of several recent wargames, but full, custom made solo systems that play with different rules than a real opponent, but manage to simulate one (the bot approach I normally find lacking because is both too complex and the decision tree too transparent, breaking the feeling of dynamic opposition).
Finally you have the two currently heavyweights (in a physical sense):
Kingdom Death Monster
Gloomhaven
I haven’t gotten to play Gloomhaven a lot yet, so I’ll withhold my judgement for now (I’m just unsure and need to try it more, I think). but as you can see people love it around here! I do love Kingdom Death Monster as a solitaire experience (and I think I would loathe it as a MP experience), but I would never recommend it at the current going price. It’s also kind of weird in how it mixed old school bookeeping and more modern design sensitivities, and some people bounce hard off it.
These offer a middle ground between the dynamic wargames that simulate a real, same decision level opponent, and the more pressure-system driven games of the first list.
I also own Robinson Crusoe, First Martians and Race for the Galaxy, but I don’t think those are as good solo as the games mentioned above.
And I just ordered the Replicators expansion for Space Empires 4X, which has a full on solo mode that I’m dying to play. But I have no idea how it will turn out.