Below is a list of players which I consider to be the best that have ever played the game...

The Men                                                                                                        The Women

#1--Young Tom Morris
Won four consecutive Open Championships (1868-1872)
Won his first Open at the age of 17
It is said that he was too good for any and all competition that was available to him
Scored the first hole-in-one in Open history
After winning the Open three years in a row, he became the owner of the Championship Belt, this led to the
creation of the Claret Jug...which replaced the Belt as the award that went to the winner of the Open
Died at the young age of 24

#2--Bobby Jones
Was an amateur golfer for his entire career
Won 13 of the 20 major championships he competed in
Won the "Grand Slam" in 1930, the only player to do so
Won 9 of his 10 Walker Club matches
Retired from golf at the age of 28
Co-Founder and co-designer of The Masters
The USGA's annual sportmanship award is named after him

#3--Ben Hogan
64 PGA Tour wins (#4 all-time)
9 major championships (#4 all-time), including the career grand slam
Involved in a major car accident in 1949.; Doctors thought he would never walk again
Was back on the course in 1950
1953 season is one of the greatest of all-time, he won all three of the majors he entered
Author of  "Five Lessons: Modern Fundamentals of Golf"
Known as the best ball striker ever

#4--Jack Nicklaus
The "Golden Bear" ranks #3 in PGA victories (73)
Ranks #1 in major championships (18), including career slam
Has a lucrative golf design business, is the author of many golf books
Host the Memorial Tournament at his home club, Muirfield Village in Columbus, OH
Best Season 1972--7 wins, 2 majors

#5--Tiger Woods
Currently has 79 PGA Tour wins (#2 all-time) and 14 majors (#2 all-time)
Has the career grand slam and the "Tiger Slam"
His 2000 season is regarded as one of the best of all-time
In 2000, won 3 majors, 9 events, and set or tied 27 Tour records
His 2008 U.S Open victory is already legendary for winning with injured leg

#6--Arnold Palmer
"The King", 62 PGA victories (#5 all-time), including 7 major championships
Largely responsible for golf explosion in the early 60's
Many business ventures including Bay Hill Golf Course and Latrobe Country Club
Has a drink named after him, The Arnold Palmer (lemonade and iced tea)
Best season was 1962---8 wins and 2 majors

#7--Sam Snead
82 PGA wins (#1 all-time), including 7 majors
In 1965, became the oldest player to win on the PGA tour (almost 53)
Won 11 events in 1950
Long driver and hence nicknamed "Slammin' Sammy"
At age 67, shot a 66 in a PGA event to become the youngest player to shoot his age
Wrote several books and instructional articles
Oldest player to make a cut at a major---1979 PGA Championship at at 67
First PGA tour win 1936, last PGA tour win 1965

#8--Walter Hagen
45 PGA tour victories (#8 all-time), including 11 majors (#3 all-time)
Prominent figure in gaining acceptance and respect for professional golfers
Best Season: 1924, 5 wins, 2 majors
Won 4 straight PGA Championships 1924-1927 and 5 total (most all-time)
6 time Ryder Cup captain

#9--Byron Nelson
52 PGA wins (#6 all-time), including 5 majors
Retired at 34 to become a rancher
1945, won 11 consecutive tournaments and 18 total; including a major
Is called the game's finest man by many
TV announcer for many years
Mentor of Tom Watson

#10--Tom Watson
39 PGA tour wins, including 8 majors
Won 5 British Open Championships
1977 victory at Turnberry is considered the greatest tournament ever played
Current Champions Tour player
Author and course designer

                     PGA Tour 
wins  Majors

11        Gene Sarazen    39        7        winner of the career grand slam; hit the "shot heard round the world"; invented sand wedge

12        Gary Player        24        9        One of the "Big Three"; The Black Knight; could easily be ranked as high as #6

13        Harry Vardon       0         7        Best player in the world in the late 1890's early 1900's; 1/3 of the "Great Triumverate"

14        Phil Mickelson    42        5         could move higher if he can pick up some more wins and majors 

15        Lee Trevino         29        6        Racked up 6 majors versus some of the best competition ever

16        S. Ballestaros       9        5        The best european of the modern era             

17        Nick Faldo           9         6         2nd greatest European of the modern era   

18        Billy Casper        51        3         battled the greats of the 60 and 70's and more than held his own    

19       Raymond Floyd   22       4         great player for a long period of time  

20       Ernie Els              19        4         has won major championships in three different decades

21       Cary Middlecoff   40       3          dominant player in the 1950's

22        Peter Thomson    6        5         dominated the British Open, hung tough versus Nicklaus, Palmer etc in the majors         

23       J. H. Taylor          0         5         member of the "Great Triumverate"
24       James Braid         0         5         member of the "Great Triumverate"           

25       Bobby Locke      15        4        banned from the PGA for a few years, but still dominated the field when he got a chance