Two games immediately come to mind when I start prepping for an open-ended campaign: D&D and Star Wars. I currently run 5th edition D&D, so that would be my go-to choice, but I would run a campaign using B/X, BECMI, or Rules Cyclopedia D&D if my players wanted me to. I’d probably even be willing to run a campaign of house-ruled 2nd edition AD&D (in fact, I was planning on it before I played 5th edition). I would not go back to 4th edition or 3.X/Pathfinder for a long-term campaign and would be reluctant to run either one of them even as a one-shot.
Now, for Star Wars, the last time I ran an open-ended campaign was for West End Game’s d6 Star Wars, and I would do so again. I would also run an open-ended campaign for Fantasy Flight Games’s version, though the last campaign I ran using that system was NOT open-ended (it was intended for a short, 6-8 session campaign).
There are other games I’m interested in trying in an open-ended campaign, but as yet, have not done so: Hollow Earth Expedition, Pulp Cthulhu, something post-apocalyptic, something superheroic… maybe some day.