At the risk of sounding Clintonesque, what shorts you want depends on what you mean by "multi purpose." The shorts I gravitate to are comfortable, minimize certain body parts, hide dirt well, and dry quickly. I also stay away from shorts with anything less than a six-inch inseam.
If you're looking to bring only one pair of shorts while hiking the Appalachian Trail or fishing for a week in Alaska, try Redington’s Tideland Short ($40; redington.com). The Tidelands are waterproof khakis designed for fly fishing. They're breathable, Durable Water Repellent-coated, well-vented, and give great coverage with a ten-inch inseam. If you're on a thru-hike and shrink a size or two, their adjustable waistband will come in handy. They've also got six pockets, two of which have zippers, that allow you to stash everything from a few emergency bills to a box of flies.
If you plan to wear your shorts hiking, gardening, or even for quick bike maintenance, The North Face Women’s Lotus Cashmere Canvas Shorts ($35) are a great choice. I’ve had a pair of these simple pigment-dyed canvas cotton shorts for a few years, and they’re the legless version of my favorite work pants—tough and fun to wear. They hit high on the thigh with comfortable side-entry pockets, and with a low-riding waist and UPF-50 rating, they're my go-to shorts for hiking and camping. The only downside is that, as cotton, they don’t dry as quickly as synthetic shorts.
If by multi-purpose you mean fun shorts to pull on after a day at the beach or for a run to the grocery store, look no further than Horny Toad’s Birdwalk ($35; hornytoad.com). They're 98 percent organic, two percent spandex, and with madras print and an angled back yoke, you'll feel as good as you look.