Without WW1, the great depression happens sooner. Probably in at some point between 1914 and 1916. (There is quite alot of evidence that the world economy was reaching its limits in 1914.) The reason for this is simply the nature of the gold standard - it acted to constrict the money supply and hence economic activity. Most likely it would be a gentler great depression though, since without the experience of hyperinflation countries had due to the economic damage caused by the war and the Versailles peace, governments will be more willing to adopt "Keynesian" policies.
Without a *WW2, the depression would likely last longer though. But then, this longer, gentler great depression would still be far, far better than what happened OTL.
Argentina is going to follow much the same trajectory as it did in OTL. The Argentine economy was based on agricultural work by low-skilled low-waged immigrant labour and the Argentine education system reflected this. Since there was no need to educate the peons, the upper and middle classes would continue to resist attempts to reform the Argentine education system. And it is the education system that in the long run determines the economic development of a country. So an uneducated Argentina will be rich during booms and poor during busts and develop slowly in the long run. The biggest thing that could change with Argentina is whether Peron or someone like him introduces a "Peronism". All the drivers for the emergence of *Peronism will still be there though.
Without WW1, the Empires will not be discredited. So while there are still plenty of opportunities to mess things up, I would say that so long as full-scale industrialized warfare is avoided, all of the Empires would slowly reform without any catastrophic breakups. Austria-Hungary would transit into a Danubian Federation, the Ottoman Empire would slowly evolve into a constitutional monarchy much like those in Central Europe. The Russian Empire would reform and improve, Poland and Finland will enjoy significant autonomy under the Tsar, the other parts of the Empire get much less autonomy, and there will likely be an uneasy see-sawing between the forces of nationalism and russian assimilation over the next 50 years. Most likely Russia will be as economically successful as the Soviet Union was over the same period, but with alot less loss of life and repression (the Tsar's government wasn't nice, but it was saintly compared to the Bolsheviks). The Ottoman empire is likely to be as successful as Turkey was on a per-capita basis, but it will have most of the population of the middle east to do it with - also, absent WW1, places like Cyprus, Kuwait and Egypt will still be technically Ottoman co-condominiums with Britain - very hard to say what that will result in, but either way, the British Empire gets rolled back a bit.
No World War 1 also means we could have practical solar power introduced much earlier. OTL, the first practical solar power plant was designed just before the war, the inventor then died fighting for King George in the trenches, and his work wasn't rediscovered until the late 1990s. Most likely that is just the tip of the iceberg as far as technological developments the war cut short.
Nuclear power will likely be developed as a marine and civil electrical power plant first, with enormous benefits as far as the development of practical atomic power, rather than atomic power built to efficiently produce plutonium for more bombs. My guess is that Britain and Germany produce the first experimental power plants in the late 40s, with nuclear power and nuclear bombs being developed by all the powers by the early 60s.
Space technology could be very interesting if satellites are developed before transistors arrive... My guess is that the transistor still comes before satellites though. So most likely all of the major powers will have France/India style space programs with workhorse rockets launching useful space gubbins. Most likely there will be several space races occurring in amongst that, much like countries had battleship races. Certainly more countries launch men into orbit. We might have a couple space stations by the 60s and a couple moon landings by the late 70s...
The US is going to be massively changed. No WW1 means Woodrow Wilson doesn't push through the raft of reforms that he did OTL to centralize power in the President and Federal Government's hands, since absent the war, he won't need those central powers. That means the States have much more importance over the long term development of the country. Not to say that the centralization of the US will be stopped, it will just continue at the same pace it did without the war. There will be bursts caused by events like the great depression which will see Progressive politicians advocating (and winning) greater powers for Washington, just as FDR did. The development of the suburbs and the use of federal power to lift poor Americans into the middle class will probably not happen. Rather America will follow a path somewhat between what happened in South America and Europe, where South American levels of wealth disparity continue to be accepted, but good education systems ensure a high degree of mobility, with rail commuter towns developing around well-developed cities.
Not to say things will all be roses though. I think the various colonial empires will continue racking up human rights abuses (I can see the Italians continuing their genocidal policies in Libya for example, and I think absent the world wars that Britain will fight harder to keep India), civil rights in the US is going to be retarded by as much as a generation and probably there will be several wars and proxy wars in the colonies, as rising powers try to dislodge established powers (think a very multi-polar version of our cold war).
fasquardon