Even in a densely populated region like New England, there are still places where it’s perfectly legal to pitch a tent for free, if you’re willing to put up with a total lack of civilized amenities. Most such places, unsurprisingly, are in the less crowded northern states. Here are a few of them. Note: It would be a good idea for you to double-check before going to any of these places, to make sure they’re still open. Conditions change from time to time, as land-management policies change or as sites are damaged by storms and other natural phenomena.
(Wherever you camp, whether at an established campsite or in a pristine wilderness, try to Leave No Trace.)
Mahoosuc Range, NH/ME A northeastern spur of the White Mountains, the Mahoosuc Range is mostly in private hands but remains quite wild. There are designated free camping areas at Trident Col, Gentian Pond, Carlo Col, and Fulling Mill Mountain, with leantos at the latter three sites. A fifth campsite, Speck Pond, has a caretaker during the summer and charges a camping fee.
White Mountain National Forest, NH/ME In the national forest, you can camp off-trail in most places without paying a dime. Many trailheads have parking fees, but not all of them–and if you have a friend drop you off, you don’t have to pay the parking fee anywhere. Hundreds of square miles of free camping here, for people who are willing to go off-trail. Check out the details here.
Green Mountain National Forest, VT Like the White Mountain National Forest, the Green Mountain National Forest contains vast tracts of land that are open to off-trail primitive camping. Details here.
Mount Mansfield State Forest, VT Camping allowed below 2500′ elevation with certain restrictions.
Four Ponds Public Reserved Land, ME A leanto and a campsite, primarily used by hikers on the Appalachian Trail.
Bigelow Preserve, ME There are numerous established campsites in the Bigelow Public Reserved Land, including several sites along the shore of Flagstaff Lake and several others up on the Bigelow Range, one of Maine’s most prominent mountain ranges.
Dead River Public Reserved Land, ME Campsites are available both on the shore of Flagstaff Lake and at a road-accessible campground at Big Eddy on the river a little below the dam.
Moose River Bow campsites, ME Free campsites are located every couple of miles along the 34-mile route of the Moose River canoe trip. Most of them are boat-access only, of course.
Chain of Ponds Public Reserved Land, ME Natanis, Long, Bag, and Lower Ponds lie along Route 27 northwest of Eustis on the way to the Quebec border. There are several sites for waterfront primitive camping, if you’ve got a boat.
Little Moose Public Reserved Land, ME Seven campsites on three ponds just west of Greenville.
Sugar Island, Moosehead Lake, ME There are several campsites on the northeast shore of the island.
Eagle Lake Public Reserved Land, ME Numerous water-access-only sites along the shore of a long, narrow lake.
Scopan Lake Public Reserved Land, ME There are four established campsites (water access only) on the eastern shore of this wishbone-shaped lake (also known as Squa Pan Lake) way up in Aroostook County.
Scraggly Lake Public Reserved Land, ME Five individual campsites (some with road access) and one campground with numerous sites, on a lake northeast of Baxter State Park.
Vaughan, Trott, and Cape Islands, Kennebunkport, ME Boaters can camp on these three islands, which are owned by the Kennebunkport Conservation Trust, but you have to get a permit in advance at the Kennebunkport police station, and you have to agree to abide by their leave-no-trace guidelines. See the KCT website for details.
Cow Island, Casco Bay, ME The island is privately owned by an organization that runs youth programs there, but they allow camping on the northwest side of the island, if you reserve a spot ahead of time. See their website for details.
Little Chebeague, Bangs, Crow, and Jewell Islands, Casco Bay, ME These islands are all managed by the Maine Bureau of Parks and Lands, and camping is allowed, though campfires are allowed only with a permit.
Crow Island, Harpswell, ME This small, wooded island is owned by the Harpswell Heritage Land Trust. Camping is permitted–see their website for details.
The island off the mouth of Strawberry Creek, Harpswell, ME Boat access only, though the mainland is just a short mudflat away at the lowest tides. Bring your own water, as for most island camping.
Little Snow Island, Harpswell, ME A publicly-owned island with several campsites on it.
Bird Island, Bowdoinham, ME A tiny island in Merrymeeting Bay, with just about enough room for one tent. No amenities.
Goat Island, Phippsburg, ME A very small island in the tidal portion of the Kennebec River downstream from Bath.
Perkins Island, Georgetown, ME A larger island a few miles south of Goat Island.
Erratic Island, Georgetown, ME A smaller island in an inlet off Hockomock Bay.
Fort Island, Boothbay, ME A state-managed island with several campsites, in the Damariscotta River northeast of Boothbay Harbor.
Donnell Pond Public Reserved Land, ME A nice cluster of lakes and small mountains, with about eight water-accessible campsites. Website here.
Cutler Public Reserved Land, Cutler, ME Walk a few miles in; bring your own water. Few camping opportunities on the East Coast are as spectacularly wild as this. Sea cliffs, cobble beaches, heavy surf, cold water. Fog. Seals. Mosquitoes.
Duck Pond Public Reserved Land, ME Three car-camping locations and three backcountry camping sites on three smallish lakes in the middle of nowhere. Web page here.
Machias River, ME There are nearly two dozen campsites scattered along the length of the Machias River corridor, most of them accessible only by boat. Bring your canoe or kayak and your Class III paddling skills!
Rocky Lake Public Reserved Land, ME A nice road-access campsite on a pristine, undeveloped lake. Bring DEET. Popular with anglers.
St. Croix River, ME Lots of free campsites for people doing the river trip. The ones on river left are in New Brunswick and thus are theoretically off-limits to US Americans. But there are plenty of sites on river right as well. Bring your canoe and your Class II paddling skills.
Penobscot River Corridor, ME The upper portions of the West Branch are accessible only by passing through a checkpoint and paying a fee to the private landowners who maintain the road system in the North Maine Woods. But the part of the West Branch south of Baxter State Park has some free campsites.
Debsconeag Lakes Wilderness Area, ME Made available for recreational use by the generous folks at the Nature Conservancy.
Nahmakanta Public Reserved Land, ME A sizable preserve centering on Nahmakanta Lake, southwest of Baxter State Park, but also including several smaller ponds with campsites on them. Abuts the Nature Conservancy’s Debsconeag Lake preserve. Map here.
Saco River, ME Camping is permitted on sandbars and beaches on the Saco between Swan’s Falls Dam and the village of Hiram. Boat access only. Campsites tend only to exist at low-water times of year, and the river sees a lot of traffic–it’s not a true wilderness experience by any means!
Windyhurst Campsite, Westmoreland, NH Boat access only–see Connecticut River Paddlers’ Trail website for details.
Wantastiquet Campsite, Hinsdale, NH Boat access only–see Connecticut River Paddlers’ Trail website for details.
Stebbins Island Campsite, Hinsdale, NH Boat access only–see Connecticut River Paddlers’ Trail website for details.
Clarksburg State Forest, Clarksburg, MA One designated backcountry camping area with tent platforms. Info here.
Mount Greylock State Reservation, Lanesborough, MA In addition to a roadside campground that’s free in the off-season, Mount Greylock has several leanto-type shelters in the backcountry which are free year-round, and where you can also pitch a tent. Website here.
Mount Everett State Reservation, Mount Washington, MA Free camping at designated sites along the Appalachian Trail.
Mount Washington State Forest, Mount Washington, MA Backcountry camping is apparently free at designated sites. I haven’t camped there.
Bearsden Conservation Area, Athol, MA Has a cabin that’s reportedly available for overnight use with prior permission. Tent camping is also apparently allowed, again with permission from the conservation area’s caretaker.
Belter’s Campsite, Sharon, CT On the Appalachian Trail a little south of the Route 112 trailhead.
Caesar Road Campsite, Sharon, CT On the Appalachian Trail in (or near?)Housatonic Meadows State Park.
Silver Hill Campsite, Cornwall, CT On the Appalachian Trail, about half a mile south of the junction with Route 4.
Stony Brook Campsite, Kent, CT Just half a mile up the trail from Stewart Hollow Brook (see below).
Stewart Hollow Brook Shelter, Kent, CT On the Appalachian Trail close to the west bank of the Housatonic River.
Mount Algo Shelter, Kent, CT On the Appalachian Trail on the ridge just west of the center of Kent.
Schaghticoke Mountain Campsite, Kent, CT On the Appalachian Trail in the Taconic Range. The water source is reportedly unreliable in dry years.
Ten Mile River Leanto, Kent, CT A nice shelter on the Appalachian Trail, just east of the New York state line near the confluence of the Ten Mile and Housatonic rivers.
Atlas of New England 
anywhere near a swimable river pool that is far away from usual hikers. I am looking for somewhere likely not used before.
People have been living, hunting, and fishing in New England for about ten thousand years, so you’re not likely to find a spot where nobody at all has camped before. But, if by “likely not used before” you mean “not showing obvious signs of previous visitors,” it should be easy. Look at a topographic map of the White Mountain National Forest–one that’s detailed enough to show not only roads but also trails and rivers and brooks. The USGS National Map Viewer is good for this. Scan for places where a brook drains a fairly large area, especially one whose headwaters are on a fairly high mountain, so it will have water even in the summer. Look for a place a mile or more from any road, where the contour lines aren’t too close together. Those closely crowded lines indicate steep areas where you may have trouble finding a level-enough spot to camp. Doublecheck the regulations to make sure that the place you’re thinking about allows dispersed camping. You can’t camp on the eastern flank of Mt. Washington, for instance, or inside the state parks. Most of the national forest is fair game, though. Then go and camp! If your site is 200 feet off the trail and 200 feet away from the water, it’s likely to be both private and pristine. (Just remember to practice “Leave No Trace” techniques, to keep it that way!)
If you want not just your tent site but also the swimming hole to be far away from other hikers, be prepared to bushwhack. There are plenty of trailless mountain brooks in the national forest, for people who don’t mind slogging through the undergrowth to find a private swimming hole.