The best adventure games like Infamous are Prototype, Marvel's Spider-Man and Crackdown. Below are 8, each with the reason it is here — and, at the end, what filtering to adventure costs you.
Filtering to adventure means the place and the story are what you want back, not the challenge. It is the right filter when the thing you remember is where you were rather than what you did.
What you get: A world with a reason to wander it, and writing that survives being read rather than skipped.
What made Infamous worth playing in the first place is covered on the full list. This page is the adventure part of that answer, and only the adventure part.
The other open-world superpower game of that era, meaner and more chaotic.
The best traversal in any open-world game, with the same rooftop rhythm.
Agility orbs turned climbing a city into the actual progression loop.
Superpowers grafted onto an open city, played entirely for comedy.
Movement built on falling in any direction you choose — strange and hard to put down.
For the grapple-and-glide loop and a city that feels built for it.
The direct successor if you simply want more of it with better powers.
Grapple and wingsuit traversal at absurd scale.
Mechanical depth. Several of the best adventure games have combat that is deliberately unsatisfying, because they want your attention somewhere else.
Specifically, these are strong answers for Infamous that are not adventure games, so they are not on this page:
The full list is on games like Infamous — 9 picks, no genre filter.
Prototype. The other open-world superpower game of that era, meaner and more chaotic.
No. Infamous released on the PlayStation 3, 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.
Anywhere the story and the place matter more than the skill ceiling — point-and-click, walking sims, narrative thrillers and most open worlds. The label alone tells you very little, which is why each pick here says what it actually is.
They split hard. Open-world adventures run to a hundred hours; the narrative ones are often finishable in an evening, and the short ones are usually the better written.
By hand. Each pick was written for the full Infamous list first, on what the game actually does, and this page is the part of that list that is adventure — 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 adventure guide for where to start in the genre generally.