Floyd Mayweather Jr Ricardo Lopez Kid Gavilan Young Griffo Roy Jones Jr Are the best fighters I know who are not great IMO.
For Great to mean something, you need to have a standard. Mine is the sport (in its current form) has being going roughly for 130 years; a Great will only come around, on average, every five years or so, that means there are roughly 26 Great fighters (even that is a bit too high IMO; it should be nearer 20), but that is the standard I use, thus none of them fighters have reached greatness.
Some not mentioned yet, I think: Del Flanagan----Sandy Saddler, Beau Jack, Willie Pastrano, Johnny Bratton, Kid Gavilan, Johnny Saxton, Virgil Akins, Ralph Dupas, Jackie Graves, Ramon Fuentes, Lester Felton, Tiger Jones, Gil Turner Tiger Jones--Sugar Ray Robinson, Kid Gavilan, Johnny Bratton, Joey Giardello, Danny Womber, Bobby Dykes, Ernie Durando, Charles Humez, Wilfie Greaves, Chico Vejar, Rory Calhoun Gil Turner--Beau Jack, Ike Williams, Johnny Saxton, Gene Fullmer, Virgil Akins, Bernard Docusen, Del Flanagan, Joe Miceli, Bobby Dykes, Ramon Fuentes, Pierre Langlois, Charley Scott, Charley Fusari Rex Layne--Jersey Joe Walcott, Ezzard Charles, Bob Satterfield, Turkey Thompson, Cesar Brion, Joe Kahut, Bob Dunlap, Grant Butcher, Willie Bean, Bob Garner, Henry Hall, Dave Whitfield
Luisito Espinosa anyone? Kennedy McKinney (TKO 2) Raul Perez (KO 1) Khaokor Galaxy (KO 1) Carlos Alberto Ramon Rios (39-0) Then you could toss any number of other fighters in there. Medina, Soto, etc.
Might get some flack for this, but maybe Trevor Berbick. Wins over: John Tate Muhammad Ali (old and faded, of course) Greg Page Mitch Green Pinklon Thomas Iran Barkley Decent enough names to have on a resume, I guess.
Winner. :good Good calls also on Sumbu Kalambay and Gil Turner. I'd also nominate Billy Graham. Had wins over Kid Gavilan, Joey Giardello, and Carmen Basilio. Sammy Angott beat Bob Montgomery three times, Ike Williams by stoppage, Willie Pep (the first man to do so), and Lew Jenkins, among others, yet is almost never talked about as though he was a great fighter. Paddy DeMarco beat Sandy Saddler twice, Billy Graham, and Jimmy Carter.
There was a journeyman from around the early '50s named Don Williams, who beat several future Hall of Famers - Ike Williams, Bob Montgomery, Lew Jenkins, maybe one or two others.
How about Orlin Norris? Probably won't be considered an ATG, probably most remembered for being spanked by Tyson and Vitali, but has wins over: Renaldo Snipes Jesse Ferguson Greg Page Oliver McCall Adolpho Washington Decent names, all of them. Decent.