Some of these have been posted before. (Thanks to Greg Slye for his work in creating this list).
Summer Interns: Museum of American History, Washington D.C. (Feb. 1 deadline)
Interns, American Labor Museum, Haledon, NJ
Internships, Celebrate New Jersey, Bridgewater, NJ
Internships, Wheaton Arts and Culture Center, Millville, NJ
Internships, Allaire Village, Farmingdale, NJ
Self-Sufficient Farming Internship, Howell Living History Farm, Howell, NJ
Internships, Morris County Historical Society, Morristown, NJ
Internships, National Archives, Washington D.C. and regional sites
Internships, New Jersey State Museum, Trenton, NJ
Education Internship, Stickley Museum at Craftsman Farms, Morris Plains, NJ
Keystone Summer Internships, Pennsylvania Historical and Museum Commission, Harrisburg, PA
Multiple Internships, Heinz History Museum, Pittsburgh, PA
Summer Internships, Gettysburg National Military Park, Gettysburg, PA (December 31 deadline)
Internships, National Museum of African American History and Culture, Washington D.C.
Internships, Smithsonian Center for Folklife and Cultural Heritage, Washington D.C.
Internships, Smithsonian Institution Archives, Washington D.C.
Internships, New Jersey Historical Society, Newark, NJ
Multiple Internships, Maryland Historical Society, Baltimore, MD
Internships, Maryland State Archives, Annapolis, MD
Museum Education Internship, Fredericksburg Area Museum and Cultural Center, Fredericksburg, VA
Internships, Lost Towns Project, Annapolis, MD
Internships, New York Historical Society, New York, NY
Internships, Albany Institute of History and Art, Albany, NY
Internships, Old Sturbridge Village, Sturbridge, MA
Multiple Internships, Litchfield Historical Society, Litchfield, CT
Internships, National Museum of the American Indian, New York, Washington D.C., and Maryland
Internships, Navy History and Heritage Command, Washington D.C.
Multiple Internships, National Holocaust Museum, Washington D.C.
Multiple Internships, Hopewell Furnace National Historical Site, Elverson, PA
Internships, NJ National Guard Militia Museum, Sea Girt, NJ
Internships at Ohio historical and cultural sites
Archival Internships, Rutherford B. Hayes Presidential Center, Fremont, OH
Internships, John F. Kennedy Presidential Library and Museum, Boston, MA
Multiple Internships, The Strong Museum, Rochester, NY
Internships, Lancaster County Historical Society and President James Buchanan’s Wheatland, Lancaster, PA
Internships, Chester County Historical Society, Westchester, PA
Internships, Army Heritage Center, Carlisle, PA
Internships, Pennsbury Manor, Morrisville, PA
Internships, York Heritage Trust, York, PA
Internships, Cumberland County Historical Society, PA
Internships, Historical New England, Boston, MA
Internships,The Heritage Foundation, Washington D.C.