Agree with Fritz on "Birds of Chile" by Jaramillo.
For South Asia there is "Birds of India" by Grimmett & Inskipp. This covers India, Pakistan, Nepal, Bangladesh, Bhutan, Sri Lanka, and the Maldives. There is also the large two volume "Birds of South Asia. The Ripley Guide" by Rasmussen and Anderton.
For South East Asia try "A Guide to the Birds of South East Asia" by Craig Robson. This covers Thailand, Peninsular Malaysia, Singapore, Myanmar, Laos, Vietnam, and Cambodia. Robson's "Birds of Thailand" is also good, but is really a condensed version of his other work covering Thailand only.
For the China region there is "A Field Guide to the Birds of China" by MacKinnon & Phillipps. This book is largely a pioneering work for the region and often comes in for very harsh criticism by birders who insist on trying to compare it to field guides from other areas. If you accept its limitations as a pioneering work then it is still a very useful guide to the area. Indeed the Mandarin version of this guide has brought birding to millions of Chinese people. The book also covers Taiwan. There is a Taiwan field guide "Birds of Taiwan" by Wu but it is in Mandarin. The plates are good and it does have English common names but at fifteen it's beginning to show its age.
You may also want to look at "A Field guide to the Birds of Borneo, Sumatra, Java, and Bali" by MacKinnon & Phillipps and "A Guide to the birds of the Philippines" by Kennedy & Gonzales.