Easy: Trail #63 to Lake Helen, Cloud Peak Wilderness/Bighorn National Forest
Look "beginning backpacking" up in the dictionary and you'll find this trail. It's well marked, has just the right amount of people on it and the views are incredible. Best of all, it gives you the option to spend as many nights as you want, without carrying a heavy pack from campsite to campsite. Hike five miles in to Lake Helen, where fish are plentiful, and set up your base camp. Enjoy yourself for a night and then hike back out, or, if you have a few more days to kill, do day hikes, using the lake as your base (i.e. you don't need to set up camp anew every night). Mistymoon Lake is just a bit farther up the trail (and also happens to have good fishing), while Lake Solitude is about another mile on. If you want to make sure you arrive back to camp tired one night, loop a few of the area's trails together: at Lake Solitude jump onto trail #120 until that hits #66. Turn east onto that trail and you'll soon be back at Mistymoon Lake and only a few hundred meters from your cozy camp. Camping in the Cloud Peak Wilderness is free, but rangers ask that you do register at the trailhead – where you're going, how long you plan on staying, the number in your party.

Intermediate: Marion Lake, Grand Teton National Park
Marion Lake sits at nearly 10,000 feet in the southern end of Grand Teton National Park. You could hike the nine miles back to it from the Granite Canyon trailhead – the trail is long, but not that steep, at least until the very end – but why when you could have the tram at the Jackson Hole Mountain Resort do all the hard work? Take the tram up to the 10,450-foot summit of Rendezvous Mountain and follow a trail 4.5 miles down the backside of that mountain and into the western end of Granite Canyon where Marion Lake is tucked under a cliff band. There are three designated campsites there, all undeveloped. When you're ready to head back to civilization, you can hike down Granite Canyon (a day's walk), or head north two miles along the Death Canyon shelf, spending another night out, before dropping into Death Canyon and walking the seven miles to the Moose-Wilson Road. For the truly ambitious, you can continue even further north along the Death Canyon Shelf and hit much of the 40 miles of the Teton Crest Trail. While it is free to camp at any of the backcountry sites in Grand Teton National Park, camping permits are required.

Advanced: Highline Trail, Wind River Mountains, Bridger Teton National Forest
I'll say it right now. The debacle I wrote about above was my first attempt at this five- to seven-day hike. And I didn't make it. But it's not undoable; I was just ill prepared, mentally and physically. I wasn't ready for an advanced backpack. If you are, though, this is the best in the state. Chances are, you'll go days without seeing another person; some days you might not even see a trail. You will see nearly the entirety of Wyoming's largest mountain range, complete with remote lakes teeming with fish (hiking with a fly rod wouldn't be a bad idea), glaciers, 11,000+ foot passes, and 40 named mountains that soar higher than 12,000 feet. You can do this trip in as little as five days, but I wouldn't recommend it. Take a week and your feet and shoulders will appreciate it. As will your eyes and soul – the more time you have to savor this scenery and the simplicity of carrying all you need on your back, the better.