There is no correct answer to the question, in part because people can't agree on the criteria.
For example, if we were to focus on the RBs who were most brilliant during their primes (and disregarded their other years), names like Gail Sayers, Bo Jackson, and Earl Campbell would deserve mention.
John Brockington, a power back, played like the Incredible Hulk for a few years on some crappy Packers teams in the early 1970's. He was remarkable, given how bad the rest of his team was. He deserves to be on somebody's top 25 list (maybe of power backs, along with guys like Christian Okoye).
Anyway, here's Gil Brandt's list:
Gil Brandt's 25 greatest NFL running backs of all time
25. Joe Perry
San Francisco 49ers, 1948-1960 and 1963; Baltimore Colts, 1961-1962
24. Ollie Matson
Chicago Cardinals, 1952-1958; L.A. Rams, 1959-1962; Detroit Lions, 1963; Philadelphia Eagles, 1964-1966
23. Jim Taylor
Green Bay Packers, 1958-1966; New Orleans Saints, 1967
22. Larry Csonka
Miami Dolphins, 1968-1974
21. Marcus Allen
L.A. Raiders, 1982-1992; kansas City Chiefs, 1993-1997
20. Marion Motley
Cleveland Browns, 1946-1953; Pittsburgh Steelers, 1955
19. Terrell Davis
Denver Broncos, 1995-2001
18. John Riggins
N.Y. Jets, 1971-1975; Washington Redskins, 1976-1979, 1981-1986
17. Jerome Bettis
L.A./St. Louis Rams, 1993-1995; Pittsburgh Steelers, 1996-2005
16. Thurman Thomas
Buffalo Bills, 1988-1999; Miami Dolphins, 2000
15. John Henry Johnson
San Francisco 49ers, 1954-1956; Detroit Lions, 1957-1959; Pittsburgh Steelers, 1960-1965; Houston Oilers, 1966
14. Adrian Peterson
Minnesota Vikings, 2007-2016; New Orleans Saints, 2017; Arizona Cardinals 2017
13. Curtis Martin
New England Patriots, 1995-1997; N.Y. Jets 1998-2006
12. Marshall Faulk
Indianapolis Colts, 1994-1998; St. Louis Rams, 1999-2005
11. Emmitt Smith
Dallas Cowboys, 1990-2002; Arizona Cardinals, 2003-2004
10. O.J. Simpson
Buffalo Bills, 1969-1977; San Francisco 49ers, 1978-1979
9. Tony Dorsett
Dallas Cowboys, 1977-1987; Denver Broncos, 1988
8. Earl Campbell
Houston Oilers, New Orleans Saints
7. Barry Sanders
Detroit Lions, 1989-1998
6. Eric Dickerson
L.A. Rams, 1983-1987; Indianapolis Colts , 1987-1991; L.A. Raiders, 1992; Atlanta Falcons, 1993
5. LaDainian Tomlinson
San Diego Chargers, 2001-2009; N.Y. Jets, 2010-2011
4. Bo Jackson
L.A. Raiders, 1987-1990
3. Gale Sayers
Chicago Bears, 1965-1971
2. Walter Payton
Chicago Bears, 1975-1987
1. Jim Brown
Cleveland Browns, 1957-1965