Here are some of the best bird watching field guides for each continent:
North America
The Sibley Guide to Birds by David Allen Sibley is a popular field guide that covers over 800 species of birds found in North America. You can even buy the guide as two separate volumes for western and western birds. This is without doubt the best field guide for North America and is one of the top three fieldguides for anywhere in the world along with Collins guide for Europe and Robertson for Southern Africa.
Another great option is The National Geographic Field Guide to the Birds of North America by Jon L. Dunn and Jonathan Alderfer.
Bear in mind Mexico is part of North America and has much avifauna one might describe as South American
If you bird in one state only there are many suitable guides, but Sibley is a must!
South America:
Birds of South America: Passerines by Robert S. Ridgely and Guy Tudor is a comprehensive guide to the passerine birds of South America. For non-passerine birds, The Birds of Ecuador: Field Guide by Robert S. Ridgely and Paul J. Greenfield is highly recommended.
Given that each Central & South American country has a good field guide it makes sense to get the best country guide rather than the continent spanning (very weighty) guides.
Europe:
Collins Bird Guide by Lars Svensson, Killian Mullarney, and Dan Zetterström is a highly regarded field guide that covers over 700 species of birds found in Europe. It is probably the best field-guide to anywhere and also comes as an app with bird song.
“Birds of Europe” by Lars Jonsson is also a great option.
Africa:
Sasol Birds of Southern Africa by Ian Sinclair, Phil Hockey, and Warwick Tarboton is a comprehensive guide to the birds of Southern Africa. Roberts Birds of Southern Africa is more comprehensive, but is far less portable tome.
Birds of East Africa by Terry Stevenson and John Fanshawe is a highly recommended guide for East Africa.
West Africa is less well served and most North African species are covered in combination with Europe.
Asia:
A Field Guide to the Birds of China by John MacKinnon and Karen Phillipps is a highly regarded guide to the birds of China. Birds of the Indian Subcontinent by Richard Grimmett, Carol Inskipp, and Tim Inskipp is a comprehensive guide to the birds of the Indian Subcontinent.
For southeast Asia there are good guides to Malaysia and to Thailand
Australia:
Australian birders are spoilt for choice as there are three or four first class fieldguides.
Michael Morcombe’s Field Guide to Australian Birds is comprehensive and current. A personal favourite is The Slater Field Guide to Australian Birds as it is not only a comprehensive guide to the birds of Australia but very easy to carry about.
Pizzey and Knight’s Field Guide to the Birds of Australia by Graham Pizzey and Frank Knight is another popular option and The Australian Bird Guide by Peter Menkhorst, Danny Rogers, Rohan Clarke, Jeff Davies, Peter Marsack, and Kim Franklin is pretty good too.
You will need a more local guide for New Zealand as there is no comprehensive guide for the whole of Australasia.
There are many other great field guides available for each continent, and these are just a few examples. It’s always a good idea to do some research and read reviews before selecting a field guide. Moreover, for many places a field guide just for a single country makes more sense for visiting or resident birders as they will be more portable and detailed.