First evidence of intercontinental or cross-cultural trade?

Tin from Britain was used in bronze found in the middle east. And it's likely the Phoenicians were getting copper from across the Atlantic during the same time period.

Humans didn't start using iron for everything because it was better than bronze. Civilizations collapsed and the trade networks for bronze alloy materials fell apart so people switched to iron because it was readily available locally. This was around the "Fall of Troy," invasion of the Sea Peoples, roughly 1200 bc. Which is the same time that ancient copper mines in Michigan were abandoned.

Humans were originally nomadic so intercontinental trade has been going pretty much as long as we've existed. It might just stop sometimes because we get stupid every few thousand years.

Bronze age: Troy and Greece: one is in Europe, the other in Asia. The Greek states did balk at the tolls of Troy, or at least that is one of the reasons given for the war by Herodotus in The Histories.

To further detail Lev's example -- there is some evidence of cultural exchange between the Maadi culture of the Nile delta region in Lower Egypt somewhere during the middle of the Naqada period of predynastic Egyptian history, in the neighborhood of 3900-3500 BCE.

Some of the evidence for this in the archaeological record is a type of blade (referred to as the "Canaanite Blade") that shows some Palestinian influences, as well as an apparently simultaneous shift to the usage of certain copper tools rather than their stone counterparts in both this Maadi region as well as in Palestine.

Source: The Oxford History of Ancient Egypt 2003 Edition, pp54-55

I know this question is old, but the previous answers did not touch on truly intercontinental trade.

The first example of intercontinental trade has to be during the Age of Discovery. From the 15th-17th century the European nations explored beyond their borders in search of trade, and subsequently subjugation. The interaction between them and other cultures is the world's first example of intercontinental trade. The Vikings may have traded with people far beyond their borders, and even the Carthaginians may have reached the New World, but in terms of sustained trade the Age of Discovery has to be paramount.

The exploration missions of the "discoverers" from Europe were all prefaced upon finding a quicker route to the silk trade routes of Asia that Marco Polo originally discovered with his overland route. This was the impetus for European exploration and would lead to the wide spread European colonization and the development of intercontinental trade in goods previously non-existent in mainland Europe such as spices, and chocolates.

These trade routes, and the driving force behind them have to be the first examples of intercontinental trade because they actually endured and influenced history. The previous routes were short lived.

According to the Wikipedia, Egypt traded with Canaan at the time of the first dynasty and probably even before that, that's about 3000 BCE.

Obsidian was exported during the Stone Age (Neolithic) from Melos (an island in Europe) to the Near East (Asia) and Egypt (Africa). Blades, cutting tools, piercing tools, arrow heads, mirrors and artwork are made from obsidian. The trade started 13000 years ago, before the discovery of agriculture.

There is direct evidence of truly intercontinental trade dating back to approximately 1700 BC. Jack Turner, in his book Spice: The History of a Temptation, writes that a handful of cloves were found in a charred vessel in Syria. The find was remarkable in that, until modern times, cloves only grew on five tiny islands that are part of the Moluccas in Indonesia. Clay tablets located at the same archeological site reference a specific king, allowing the tablets and the cloves to be dated to approximately 1721 BC.