What private individual in the United States owns the most private
land? (in terms of acres, not in terms of value)

Ted Turner, the founder of CNN, is the largest private individual
landowner in the United States. The most recent online mention I've
found is dated May 6, 2003:

"[Ted] Turner, the nation's largest private landowner, had a net worth
of $2.2 billion last year, ranking him 80th on Forbes magazine's tally
of the richest Americans."

CNN Money
http://money.cnn.com/2003/05/05/news/turner_aol/

Here are some other sources naming Turner as the largest individual
landowner in the US:

"With approximately 2 million acres of land, Worth Magazine listed Ted
Turner as the largest individual landholder in the United States.
Turner lands are innovatively managed and work to partner economic
viability with ecological sustainability."

TedTurner.com
http://www.tedturner.com/enterprises.html 

"As the creator of CNN, the first 24-hour news network, and other
cable stations, Ted Turner forever changed the landscape of American
television. Now the 64-year-old 'media mogul' plans to change the
landscape of the American West. He is the ringleader of a giant
scientific experiment to restore damaged ecosystems--specifically, to
reintroduce species and to reinvigorate Western lands in an
economically sustainable way. And he may just have the means and the
minds to pull it off. Turner is the largest private landowner in the
nation, controlling two million acres (an area bigger than Delaware)
spread across 10 states."

Scientific American
http://www.sciam.com/article.cfm?articleID=000A7B7C-7F05-1D2B-97CA809EC588EEDF&pageNumber=1&catID=2

"Ted Turner owns more land than anyone... Ted Turner, the CNN mogul
who has sped up our sense of time and sent us hurtling into the
future, has embarked in just the opposite direction across the
American West. Since 1987, he has bought 1.7 million acres - mostly in
Montana, New Mexico, South Dakota, Nebraska and Kansas - becoming the
largest private landowner in the United States, according to Worth
magazine."

Freedom.org
http://www.freedom.org/prc/news/20000301/14.html#tt

"Ted Turner, the CNN mogul who has speeded up our sense of time and
sent us hurtling into the future, has embarked in just the opposite
direction across the American West.

TURNER HOLDINGS 

1987: Bar None Ranch, Montana, 23,000 acres. 

1989: Flying D Ranch, Montana, 113,000 acres. 

1992: Ladder Ranch, New Mexico, 155,000 acres. 

1993: Snowcrest Ranch, Montana, 13,000 acres. 

1994: Armendaris Ranch, New Mexico, 360,000 acres. 

1995: Spikebox Ranch, Nebraska, 52,000 acres. 

1996: Vermejo Park Ranch, New Mexico, 580,000 acres; Red Rock Ranch,
Montana, 5,000 acres.

1997: Deer Creek Ranch, Nebraska, 48,000 acres. 

1999: Bad River Ranches, South Dakota, 140,000 acres; McGinley Ranch,
Nebraska, 67,000 acres; Z Bar Ranch, Kansas, 35,300 acres.

2000: Double H Ranch, Kansas, 2,900 acres; Blue Creek Ranch, Nebraska,
64,600 acres.
 
Since 1987, he has bought a staggering 1.7 million acres in Montana,
New Mexico, South Dakota, Nebraska and Kansas - becoming the largest
private landowner in the United States, according to Worth magazine -
and is using his fortune to turn back the hands of time."

Billings Gazette
http://www.billingsgazette.com/region/20000312_r0grass.html

Google search strategy:

Google Web Search: "largest private landowner" + "united states"
://www.google.com/search?hl=en&ie=UTF-8&oe=UTF-8&q=%22largest+private+landowner%22+%22united+states

Google Web Search: "largest individual landowner" + "united states"
://www.google.com/search?hl=en&ie=UTF-8&oe=UTF-8&q=%22largest+individual+landowner%22+%22united+states

I hope this information is useful. If anything is unclear, or if a
link does not function, please request clarification; I'll be glad to
offer further assistance before you rate my answer.

Best regards,
pinkfreud

Excellent, very complete, good sources. Thanks!