Greatest species endemism
Who
Tropical Andes
Where
Venezuela ()
When
The area of the world considered to have the highest species endemism is the Tropical Andes stretching across Venezuela, Colombia, Ecuador, Peru, Bolivia and a small section of northern Argentina. So far, scientists have identified 20,000 vascular plants, 677 birds, 68 mammals, 218 reptiles and 604 amphibians which are endemic to the area covering 1,258,000 km² (485,716 miles²). From Consultant:
http://www.biodiversityhotspots.org/xp/Hotspots/andes/
This is the page with info on the Tropical Andes, which has 15,000 endemic plant species.
The following is pasted from that page. Note that the bromeliad they refer to is Puya raimondii, the ‘slowest-flowering plant’.

The richest and most diverse region on Earth, the Tropical Andes region contains about a sixth of all plant life in less than 1 percent of the world’s land area. One of the more unique plant species is an Andean bromelilad that require 100 years to mature.
The threatened yellow-eared parrot, yellow-tailed woolly monkey and spectacled bear are all endemic to the Tropical Andes. This hotspot also maintains the largest variety of amphibians in the world, with 664 distinct species. Unfortunately, almost 450 amphibian species are listed as threatened on the 2004 IUCN Red List.
Although a quarter of its habitat still remains, the region is facing a variety of threats including mining, timber extraction, oil exploration, and narcotics plantations, which are all expanding due to the continual growth of many large cities in the region. The cloud forests are facing increased pressure from hydroelectric dams, and invasive species like the American bullfrog and grasses for cattle grazing are becoming problems as well.