The best indie games like Zack and Wiki are Return of the Obra Dinn, The Sexy Brutale and Lorelei and the Laser Eyes. Below are 5, each with the reason it is here — and, at the end, what filtering to indie costs you.
Filtering to indie means you want the answer a small team would give. It is usually the most interesting filter on this site, because small studios take the risks large ones cannot.
What you get: One strong idea, explored completely, at a price that makes trying it easy. Indies have no production to hide behind, so the design is exposed.
What made Zack and Wiki worth playing in the first place is covered on the full list. This page is the indie part of that answer, and only the indie part.
Deduction as the entire mechanic, and it never tells you if you are right.
A repeating day full of people on schedules you have to learn.
A puzzle game where the puzzles and the story are the same thing.
A small adventure hiding an enormous amount of secret design.
The best new puzzle game in years, and it respects you.
Polish and scale, sometimes. A few of these are rough at the edges, and a big-budget pick will always look better doing the same thing.
Specifically, these are strong answers for Zack and Wiki that are not indie games, so they are not on this page:
The full list is on games like Zack and Wiki — 9 picks, no genre filter.
Return of the Obra Dinn. Deduction as the entire mechanic, and it never tells you if you are right.
No. Zack and Wiki released on the Nintendo Wii, but a recommendation is only useful if you can play it, so the picks above span platforms and eras. What they share is the genre and the reason.
Self-published, or published without a large publisher's money. It says nothing about the size of the game, which is why a forty-hour metroidvania and a two-hour art piece sit under the same label.
Constraint. Without a budget to hide behind, one idea has to carry the whole thing — and a small team can commit to something risky that a large one would sand down.
By hand. Each pick was written for the full Zack and Wiki list first, on what the game actually does, and this page is the part of that list that is indie — never a genre tag lookup, which is how "best racing games like Super Mario 64" used to be a page on this site.
Or read the indie guide for where to start in the genre generally.