You don't have to tee off to enjoy a vacation at any of the top golf resorts of the world, of course, but for confirmed players that's the name of the game. And those resorts -- which number in the dozens worldwide -- offer a myriad of challenges to the true golf addict: from the 18th hole on the Doral's "Blue Monster" course, with its 425-yard length and the lake hazard that borders the green, to the oceanfront 18th hole at the Lodge at Pebble Beach, with trees overhanging the green to add to the difficulty.

The sport originated in Scotland. In fact, the game was so popular there in the mid-15th century that the king forced his citizens to turn more to archery, so they would be able to defend their country.

In the early 1950s, after World War II and with the rising affluence of Americans, golf's popularity began to grow in this country. A major influence was the sudden visibility of champion Arnold Palmer and avid golfer President Eisenhower -- both seen on fledgling TV by huge audiences. The ensuing interest spurred the development of new golf courses directly connected to fine resorts.

Today, the warmer states like Florida, Arizona, Nevada and California boast a large number of golf courses because the weather invites year-round competition. But the resorts are widespread both in this country and abroad, among them:

* The Greenbrier, White Sulphur Springs, W.Va., with three 18-hole courses.

* The Homestead, Hot Springs, Va.; three 18-hole courses.

* Sea Pines Plantation, Hilton Head Island, S.C.; three 18-hole courses.

* Arizona Biltmore Resort & Conference Center, Phoenix; two 18-hole courses.

* The Wigwam, Litchfield Park, Ariz.; three 18-hole courses.

* Desert Inn, Las Vegas; one 18-hole course.

* Doral Country Club, Miami; four 18-hole courses and one nine-hole course.

* Grenelefe Golf & Tennis Resort, Haines City, Fla.; three 18-hole courses.

* La Costa, Carlsbad, Calif.; three nine-hole courses, which will become two 18-hole courses by June 1, after completion of another nine holes.

* The Lodge at Pebble Beach, Pebble Beach, Calif.; two 18-hole courses.

* Marriott's Castle Harbour Resort, Bermuda; one 18-hole course (hotel closed for renovation until early 1986, but the golf course is open).

* Gleneagles, Perthshire, Scotland; three 18-hole courses.

* Casa de Campo, La Romana, Dominican Republic; two 18-hole courses.

* Mullet Bay Resort & Casino, Sint Maarten; one 18-hole course.