Into the Woods is an obvious one. I also saw an outdoor production of South Pacific that worked pretty well.
I think most established shows probably CAN work outdoors, as long as it isn't super reliant on the claustrophobic feeling of being indoors - the same company that did South Pacific (Mountain Play) did Beauty and the Beast a few years later. All of their productions are performed in broad daylight - so when Belle gets lost in the woods at night, and then gets shut up in a dark, dingy castle, the effect is kind of lost. But that was largely because it was daytime, not necessarily because it was outdoors. Performing outdoors at night offers enough flexibility with lighting that it kind of doesn't matter where the show takes place.
However, if you're looking for that "next level" quality of shows that are enhanced by being outdoors (rather than just "working" outdoors), then I guess it's best to look for shows that take place in nature, or surrounded by nature, right? The Seagull is another one that comes to mind offhand
Or you can have immersive/experiential shows that were conceived to be performed outdoors from the get-go - we've seen some of those during COVID times, naturally. There's the Voyeur show that's been running for a few months now, and there was Bill Irwin's "Busking Project" which was performed on the street.