For $10,000 a week, you can rent Rex Harrison's villa on the French Riviera: One entire floor is the two-bathroom master-bedroom suite with sea view. For $4,500 a week, Princess Margaret's four-bedroom villa on Mustique with vistas of both the Atlantic and Caribbean can be yours. But don't despair if the prices are beyond your means. There are hundreds of villas and other rentals around the world, ranging upwards from as little as $250 a week. Among the most unusual:

*Do Re Mi: Perched on a hill overlooking the beach at Puerto Vallarta, Mexico, the Mediterranean-style, three-bedroom villa surrounded by palm trees accommodates six. There's a game room, large pool with bar and a private tennis court. Cost per week: $1,806 (includes maid service), plus $60 membership fee. Villas of the World, a division of American Leisure Industries Inc., 4501 Forbes Blvd., Lanham, Md. 20706, (800) 638-8976.

*Althorp: This estate in Northamptonshire, England, 80 minutes by train from London, includes a 550-acre park and is occupied by Earl Spencer, father of Diana, princess of Wales. For rent is the earl's three-bedroom Foresters Cottage, built of sandstone in the early 19th century. Deer, cattle and sheep roam in the park, and there are opportunities nearby for riding, fishing, golf and tennis. Cost per week: About $275 in winter, $390 in July and August, with an extra charge for electricity. Villas International Ltd., 71 W. 23d St., New York, N.Y. 10010, (800) 221-2260.

*Village House: A large, 18th-century French home in St. Ge'ly-du-Fesc, a charming rural village about seven miles northwest of Montpellier and 13 1/2 miles from the Mediterranean Sea. Restored and modernized in 1972, the home is occupied most of the year by its owners. The living rooms on the ground floor were once part of a medieval monastery. The property features five bedrooms; resident caretakers look after the house, pool and garden. Cost for two weeks for six persons, beginning May 18: $828 (two hours per day domestic help included; no children under 10 years). Vacances Franco-Britanniques Ltd., 1 St. Margaret's Terrace, Cheltenham, Gloucestershire, England Gl50-4DT, (0242) 526338.

*Glin Castle: The gleaming white picture-book residence, whose 500 acres of land have been in the keeping of the Knights of Glin for the past 700 years, faces north across the Shannon Estuary about 30 miles west of Limerick, Ireland. The current knight and his wife live in a separate wing of the castle. Accommodates eight to 10 people, but small children are allowed only if accompanied by a governess (delicate antiques abound). There's a new all-weather tennis court. Cost: about $4,500 a week this winter (less in summer without the heating bill); cook and two housekeepers are included in the rental, but you must add another maid if your party exceeds six, and must pay for the staff's food. At Home Abroad Inc., Sutton Town House, 405 E. 56 St., 6-H, New York, N.Y. 10022, (212) 421-9165.

*Fisherman's House: This converted three-level, two-bedroom property at Porto Ercole, Italy, 90 miles north of Rome, opens onto the old village piazza with splendid vistas of the town and the sea. It's a short walk to the port, restaurants and shops. Cost this winter for one month for six persons: $2,550 (includes electricity but not heating oil). At Home Abroad.

*Chalet-style Apartments: In Zermatt, the popular Swiss resort, towering slopes surround the old village and horse-drawn sleighs replace the forbidden auto. The apartments are near the cable cars, an easy walk from the town center with views of the towering Matterhorn.