What are some good examples of this?
D&D settings with non-D&D rulesets:
I have personally done pretty comprehensive conversions for Al Qadim and Dark Sun for Mythras. I'm also aware of a Dragonlance Mythras conversion, and I have done a small amount of work on a Planescape conversion I plan to get back to.
My conversions focus on the setting and have little regard for converting pure mechanical D&Disms, but Mythras Classic Fantasy is an official product (you can check out the free version, Classic Fantasy Imperative) specifically designed to emulate D&D.
GURPS Dungeonfantasy is another official product looking to emulate one form of traditional D&D play in it's own way.
I am currently running 1e-era Forgotten Realms using Rolemaster, and I'm not close to the first person to have done so.
Pretty much every 2-e era setting seems to have a Savage World conversion. 2e-setting communities are full of people doing and offering conversions to their preferred settings.
D&D Rules for non-standard settings/styles
Godbound is a prime example of a commercial game close enough to D&D that you can pick up and use old D&D modules with basically no conversion, but it's focusing on demigod PCs and has as much in common with Exalted as D&D.
The d20 era was full of games with D&D mechanics but different settings. Lone Wolf and Conan by Mongoose were using 80% - 90% or more of the same core mechanics as D&D, with a few tweaks, to run very different games. Even Traveller got a d20 version, and it's getting a 5e D&D version as we speak.
Conan also had an official 1e or 2e version.
And then you had 2e settings like Dark Sun and Birthright really trying to push the envelope on what D&D can be.
Apart from commercially released options, surely it's not in dispute that people have used D&D to run anything and everything they possibly can over the past 50 years?