Katamari and Portal are the last games that really had me thinking about playing even when I wasn't playing them. I wish those games had additional levels to buy.
The Talos Principle — Basically Portal but... different. Physics, timing, & world-affecting-zappy-device puzzles. No actual portals but it's pretty similar. A "there's more going on" story. Quite good.
The Witness — Myst-like I guess? In that you're exploring an island and solving puzzles and piecing together a story, kinda. But the puzzles are all variations on one sort. Elements get added, things get weird, lateral thinking becomes necessary. It's good.
Edit: Just bought Talos for the PS4! Once again, thanks! When I'm done with it, I'll check out Witness.