There is only one travel-book that you have to read about South America, and that book is "A death in Brazil" by Peter Robb.
The reason for this is two-fold.
Firstly, "A death in Brazil" is quite simply a brilliant book. This meticulously researched, deeply passionate and thoroughly absorbing work is undoubtedly the greatest work about any country south of Mexico.
But this is unfortunately something of a default achievement. Not only is "A death in Brazil" the best, but it is also the only really good work (that I have discovered, at any rate), about any part of this rich and vast continent. This dubious distinction, I should say, is not to detract from its qualities - it is one of the finest pieces of any travel-writing that I have read, cleverly switching between genuinely unique personal experience, narrative accounts of public events, and insightful socio-historical analysis that is always colloquial enough to avoid sounding like a Cultural Studies seminar.
But as far as South-American travel writing is concerned, "A death in Brazil" stands as a lush oasis in a barren literary desert.

It is possible, of course, that I am incorrect in this wholesale condemnation of this area of travel-writing. In fact, I am more than happy for someone to prove me wrong about this if it gives me something to read. (One reason that I wrote this piece is so that someone, typing "South American travel writing" into google, will come across it and let me know of a book that has slipped through my net.) Also, it is always possible that I am too harsh and hasty a critic. I tend to tolerate boring books until half-way through the first chapter. If I am still bored at that point, I stop reading and give the book away. But so far, at any rate, I stand by what I have said. I have even developed a couple of theories as to why the few books written on the subject of South America are so monumentally disappointing.

First of all, we have the question of the sheer scarcity of travel-writing about South America. Why is it so hard to find? The answer, I think, lies in the sheer size of the thirteen countries that make it up. Africa, a continent of around the same size, is divided into more than three times as many countries. The same goes for Western Europe, an area of barely half the size of either Africa or South America. It is no doubt far easier to make a really authoritative and thorough account of countries of European smallness. In fact, as far as I am aware, there is probably twice as much English-language travel-writing dedicated to Spain and Italy alone then to the rest of the world put together. The infamous Argentine trouble with developing a consistent and cohesive identity is in no small part due to its sheer size, and we can hardly be surprised that something that these South Americans themselves find so difficult to describe should have dissuaded the gringo.
The immediate question that this hypothesis raises is that of the USA. There is plenty of really good writing about "America", from John Steinbeck, through Alistair Cooke, Jack Kerouac, Bill Bryson, etc, etc. So why has the USA, with so much in common with Argentina (national myth of the cowboy or gaucho, slaughter of the indigenous population to make way for the settlers, "melting-pot" ethnic diversity) produced so much more quality travel-writing?
There are, I think, two possibilities. First of all, whilst the USA and Argentina share many historical parallels, they also have many differences. Whilst both were originally colonies, and had to fight for independence, the USA's colonial status was far less willing from the start. Many of the first settlers were famously in search of specific freedoms, and the birth of the country (for which, importantly, much more blood was spilled that in Argentina's bid for independence) was far more pervaded with a sense of liberty than that of Argentina, and this no doubt has given Americans more of a shared identity than is had by the Argentines. (The US too, has a shared identity as a nation of immigrants. Whilst many of the Argentine "Indians" were wiped out, a large part of the population is made up of indigenous immigrants from other parts of South America, meaning that the country is a strange blend of those with ancient connections to the continent, and those without).

A second point is that it is noticeable that all of the really good American travel writing is written by Americans. Perhaps one has to be born into a country of that size to really understand it. And it could be, therefore, that all of this has something to do with the fact that Americans belong to the English speaking world, in which travel-writing is a popular form, whereas Argentines belong to the Spanish-speaking world, in which it is perhaps not. I could be wrong about this, of course.
We have, therefore, a couple of tenuous explanations of why there is so little travel writing about Argentina specifically, and South America in general. But no we face a new question; Why is the little travel writing about South America that actually exists so disappointing? For there are a few books out there, the two most famous being "Saddled with Darwin" (a journey, partly on horseback, following Darwin's journey through South America) by Toby Green and "The old Patagonian Express; by train through the Americas" by Paul Theroux. Both of these men had a good budget at their disposal, plenty of free time dedicated specifically to travelling and writing about their experiences...everything, in fact, that one would think would result in great pieces of travel-writing. But despite all this, both works are completely disappointing. Or would it be better to say because of all this?
Here we come to the crux of the matter. If you look at all the really great travel-writing out there; Everything from the early "As I walked out one midsummer morning" by Laurie Lee, through the popular "Notes on a Small Island" by Bill Bryson, to the subject of all this, "A death in Brazil", one common aspect is obvious. Almost all great travel writing came about by accident. The writer travelled simply to travel, keeping incidental notes along the way, and some time afterwards (in the case of "A death in Brazil" as long as twenty years), he or she decides that, actually, it is all worth publishing. Paul Theroux and Toby Green both travelled specifically to write, the former, because that is what he does, the latter, because he had won a photography competition for which the prize was money which could be used to travel and write about the experience. (Bizzarly enough, most of the photographs in "Saddled with Darwin" do not look like the work of a professional at all).

Travelling specifically to write is a great way of producing really bad travel writing. The accidental writer, such as Peter Robb, looks down from the top of a mountain of experience and pinpoints specific illuminating incidents and adventures along the way, with the additional insight of accumulated knowledge about the national psyche, seeing all the while the broad path that his journey through a country has taken. To make that same journey with a book already in mind would be to have to document every stage of the journey without any of the perspective of the journey as a whole, and without the lens of time with which to judge which incidents to document and which to forget. This is what has happened with Paul Theroux and Toby Green, and the result is two very boring books.
There are a handful of books which don't have these specific defects, and I suppose that whilst I didn't enjoy them all that much myself, they may be enjoyed by other people. The most worthwhile is probably "The motor-cycle diaries" by Che Guevara, a sheaf of papers posthumously published by the revolutionary's daughter. This work is probably best read alongside the 2004 film. Che's raw account was not intended (in its present form, at any rate) for publishing, and there are a lot of incidents that he notes with passing modesty ("it took me two hours to swim across the river") that are actually a lot more dramatic, and which the film emphasises. There is also, of course, "In Patagonia" by Bruce Chatwin. I suppose it would appeal to some people, but the disconnectedness of each chapter from the next, which some seem to find exhilarating, leaves me bored by the lack of cohesive structure. Like so many works, "In Patagonia" excites us by "breaking the rules", but at the same time reminds us of why the rules are there.
There are a few more books out there, obscure 18th Century accounts of "Journeys in the Argentine", Darwin's own notes, etc, etc, works which are more interesting from a historical account than anything else, as well as a handful of less-than-brilliantly-written accounts that were inevitably going to happen as soon as backpackers began hitting the Gringo Trail. (In fact, "the Gringo Trail" is the title of a much hyped book that I got bored of, as usual, halfway through the first chapter.) My advise to anyone searching for good South American travel writing, therefore, is to turn to the many travel magazines popping up across the continent. There are some really great free or cheap magazines in Buenos Aires alone, full of informative, passionately written stuff, "Vos", "The Nose", "The Argentimes", etc. If you are really determined to pick up a book about the continent, however, remember that I am a harsh critic, and you may well enjoy much of the stuff that I didn't. All of the books that I have mentioned are fairly easy to get hold of, at your local book store, or, appropriately enough, on amazon*...
*See what I've done there? Amazon.com, River Amazon...see? Clever, Eh?