I've been following the Red Sox for about 43 years, so I can't say Ted Williams was my favorite player or nobody turned the double play like Bobby Doerr. So, I'll have to settle for players whom I found had a special achievement over the years. They might be great players, or just fascinating for some reason or another.
Catcher - Jim Pagliaroni; I may be hallucinating this, but somethow I think I recall listening to a game in which Pagliaroni, anything but fleet-footed, hit for the cycle.
First base - Dick Stuart, Doctor Strangeglove. Stuart hit 42 homers in 1963 and had 29 errors at first base. He was meant to be a DH. He led the AL in extra base hits in 1963, so he had to be a pretty good hitter.
Second base - Dalton Jones; Jones was one of those lefties with the sweet swing that you knew was going to be a great hitter. Only it never turned out that way, as he never had 100 hits in a season. Making matters worse was that he didn't have great range or a great glove. Still he had a key hit in the sixth inning rally that propelled the 1967 Sox into the Series.
Shortstop - Spike Owen was one of Roger Clemens contemporaries at the University of Texas. He was a solid defensive shortstop who couldn't hit (.269 his best year, career .246). Somehow Joe Morgan pinch hit Owen for Jim Rice, which may have been what I remember him best for.
Third base - Wade Boggs has to be the man. 3000 hits. Margo Adams. Chicken every day. Does Wade still eat chicken every day. The best two-strike hitter I've ever seen.
Left Field - The memories of Yaz are overwhelming. 1967, the last Triple Crown Year. Losing the batting title to Alex Johnson in 1970 by less than a point when Johnson sits out at bats knowing he's clinched it. Yeah, he popped out against Gossage to end 1978, but he made so many memorable plays in left (the All-Star catch in RFK, the Rohr one-hitter catch, throwing out guys at the plate in Fenway). He hit at least ten homers in 22 different seasons, and hit .369 in the post-season with an OPS of 1.047.
Center Field - Jose Tartabull was a speed guy with a weak arm. Yet, somehow in 1967, he summoned up a two-out throw from center to nail Ken Berry of the White Sox to allow the Sox to save a game.
Right Field - Joe Lahoud was anything but a great hitter, ending his career with a .223 average and 65 homers. But on June 11, 1969 Lahoud smacked three homers for the Sox. Have a day.
Pitcher - not even close. Bill Lee, the Spaceman. Won seventeen games three times from 1973 to 1975, and won 16 for Montreal. Got hurt in a brawl at Yankee Stadium (part of the mystique of the Sox forever) and dubbed manager Don Zimmer, 'The Gerbil'. Lee's signature pitch, 'the Leephus' also allowed Tony Perez to smash a critical homer against the Sox in the 1975 Series.
C- Bob Tillman, beaning John Wyatt with a throw to second
1B - Nick Esasky, lost forever after experiencing vertigo
2B - Marty Barrett, with an unforgettable 1986 post-season
SS - Luis Aparicio, tripping around third in 1972, unable to score, the Sox miss the playoffs by 1/2 a game
3B - Juan Beniquez played 17 years in the majors and hit .291 in the 1975 AL pennant season. I remember him most as an option in the computer simulation games of the World Series, another option versus Rico Petrocelli.
LF - Manny Ramirez displaying his American flag after earning citizenship.
CF - Gary Geiger; I don't remember him as being that productive, but from 1961 to 1963 he averaged 17 homers a season.
RF - Tom Brunansky for his season saving catch down in the right field corner.
P - Rogelio Moret, the rail-thin lefthander who developed catatonia during the season, but had 14-3 and 13-2 seasons.