World Tourism Organization (WTO) Click on "Facts and Figures."
Online statistics show no country-to-country flows. But has breakdown of country expenditures, receipts, and arrivals within regions. The publication Yearbook of Tourism Statistics does have country-to-country flows! Also, the Compendium of Tourism Statistics-2201 Edition has data from 1995-99. Available through purchase.

ITA (International Trade Administration) Statistics available from an official U.S. Government site produced and maintained by Tourism Industries office. Free online subscription.

UNESCO has International Tourism in World Culture Report available online and hardbound. Online data is not as thorough as in hardbound. For example, the hardbound shows 3 top countries of origin to visiting country—the online edition only shows the top two. Also, online shows only the years 1995/96.

USDOT International travel and Tourism Statistics is a CD-ROM "from a broad cross-section of travel, tourism and statistical agencies representing nations from every region." Press release here.