I feel like someone is trying to squirrel out of their social study assignment by getting someone (us) to do the homework for them.
Why save Tigers? There's a lot of good reason for it (ignore the propaganda by both the tree-huggers and greedy capitalists for now).
1) Population Control, this is the same reason why we try to save wolves, sharks, falcons and many other top predators. There were MANY actual experiments done (intentionally and otherwise) that prove losing/lack of top predators will cause major problem. Even the extinction of prey species cause major problems, look at the impact of wiping out the bisons from most of North America. That's why we have re-introduction programs at Yellowstone, Canadian Arctic, Rockies, even urban cities.
Here's an example of what happens when an area loses a top predator, I'm going to go with wolves since they have more data than other species.
Location - Boreal Forest with plentiful streams and creeks
Locally Extinct species - Wolf
Primary Detrimental Effect - Explosion of prey species, especially white-tail deers
Secondary Detrimental Effect - Deers no longer fear to feed near "ambush" areas, saplings and other plants are eaten clean along the ambush area (normally near waterways)
Additional Detrimental Effect - No new growth of plants in the following years, causing a lack of food for majority of the species, leading to massive die offs. No replacement of natural die off of plants. Increased erosion due to lack of any root systems. Waterways dries up, become murky or become altered significantly to cause changes in the local environment due to increased erosion and silt. Other predator become affected as source of food in the waterways are removed/altered. Overall changes in the system causes shift/decrease in annual GDP of the land. Species looking for food head "cultivated" lands in search of food, deers compete for grazing against farm animals, predators comes to farm land to seek preys, biomass cycle become disrupted, causing shifts in nitrogen fixations and other cycles that can adversely affect crops.
Tiger has a list/chart of its own, just don't want to share it directly in case this IS someone's homework xP