Direct Delta flights from SFO to Europe/S. America

You're looking for flights to anywhere as long as they are nonstops?

Barcelona has no direct flights out of SFO as far as I can see. I think Delta's only direct international flight out of SFO is to Toyko-Narita. You could fly KLM thru Amsterdam or United thru Paris Charles de Galle. United and British Airways could get you there thru London, but ground fees are very high. Lufthansa could get you to Europe thru Frankfort or Munich. Otherwise, you'd have to transfer at airports in the Eastern U.S. to get to Barcelona.

Have you considered checking their route map? http://www.delta.com/content/www/en_US/traveling-with-us/where-we-fly/routes.html According to that, they fly direct to Paris and London from SFO. South America is predominately served from their hub in Atlanta.

There are many on-line agencies competing for your business. Most if not all show the number of stops on requested routes. Look at www.kayak.com, www.skyscanner.com, and www.itasoftware.com, among others, to find collections of airlines and agencies.
By the way, in airline language, "direct" means the journey is on one aircraft, but not necessarily "non-stop".

SFO direct and non-stop to Amsterdam, Paris, Mexico City, Seoul, and Tokyo: http://delta.innosked.com/(S(rwyapfj4hxdzyt45dyri1155))/Default.aspx Amsterdam and Paris are code-share with KLM and Air France. I assume you have Delta miles you want to use? Or some other reason for asking specifically about Delta?