The best platformer games like Mega Man 2 are Mega Man X, Mega Man 11 and Shovel Knight. Below are 10, each with the reason it is here — and, at the end, what filtering to platformer costs you.
Filtering to platformer means you want the movement itself to be the pleasure. It is the right filter when the thing you liked was getting from one place to another.
What you get: A game you can judge in ten seconds. Platformers live or die on the jump, and a good one feels right before anything else happens.
What made Mega Man 2 worth playing in the first place is covered on the full list. This page is the platformer part of that answer, and only the platformer part.
The reinvention — same structure, with a dash and a wall-cling that change everything.
The modern entry, and the closest in feel to the NES run.
NES design sensibilities with modern fairness, and the best homage there is.
Made to be this era again, and unusually tough.
Mega Man X as a roguelite, and the co-op works.
An indie built on Mega Man Zero's speed and combo system.
The other great NES action-platformer, and much more deliberate.
If the precision rather than the boss order is what you liked.
NES action platforming at its most cinematic and most unfair.
Momentum platforming with the same density of ideas per level.
Weight. Platformers rarely carry a story you will think about afterwards, and the collectible-led ones can become checklists if you let them.
Specifically, these are strong answers for Mega Man 2 that are not platformer games, so they are not on this page:
The full list is on games like Mega Man 2 — 12 picks, no genre filter.
Mega Man X. The reinvention — same structure, with a dash and a wall-cling that change everything.
No. Mega Man 2 released on the Nintendo Entertainment System, 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.
Whether the move set is complete early. The great ones give you everything in the first level and spend the rest asking better questions of it; the weak ones drip-feed abilities to disguise thin level design.
Different games. 2D platformers are about precision on a single screen; 3D ones are about reading space and camera. Each pick below says which it is.
By hand. Each pick was written for the full Mega Man 2 list first, on what the game actually does, and this page is the part of that list that is platformer — 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 platformer guide for where to start in the genre generally.