The Narrows at Zion National Park is a justly famous hike. The season for the Narrows runs from late May on, depending on spring runoff. The year we did it (1998), snowpack was slow to melt and even in mid-June they were recommending against hiking it due to heavy runoff. We decided, like a lot of people, to try it anyway, and it was a great hike. We brought ski poles with us for balance, and they really helped, since the bottom of the river is covered with bowling ball sized rocks in places, and you can't see into the rushing water. Definately wear hiking boots if you don't want to get a twisted ankle.
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At the entrance to the Narrows, there were a good 100 people wading in the river, and we thought it was going to be a crowded hike. After the first turn, however, only a few hundred feet up, about 75% of the people turned back. After the first mile, probably less than 15 people kept going. The water wasn't cold at all, and even after an entire day in the shady slot canyon, with about half the time spent wading in the water, we weren't cold. There are tons of photo opportunities, and if you walk carefully in the shallowest parts, you could bring a normal camera without any problem, although a waterproof disposable worked out great for us.
Here's my wife, Kris, having a great time in the warm waters of the Narrows. The cliffs in this picture extend up another hundred feet at this point.
After 4 miles or so, the canyon really narrows, and you enter the part that it was named for. The cliffs rise 1000 feet on either side, and it's only 30 feet wide in spots. Orderville, a side canyon about 4 miles in, is really pretty, and should not be missed - it's a nice spot to have lunch, too. I won't bore you with endless descriptions of each cool rock outcropping, but let me say it's definately one of the coolest hikes I've ever been on. In the narrowest part, the sunshine is at such an angle that it only reaches the bottom for a few minutes a day, and you can actually see the shadows moving in the canyon over just a few seconds when it's close to noon.
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Another shot of Kris, in shadow against a rock, at about the furthest point up the Narrows that we got. There is a very cool waterfall cascading down 1000 feet just to her left, but you'll have to do the hike to see it.