Where did spaghetti originate?

Pasta was imported to Italy from China by Marco Polo, so it's up to you to decide.

"While many believe that spaghetti (or even pasta in some accounts) originated in China (where long thin noodles have a lengthy history), some now assert that the reading of a lost Marco Polo manuscript which led to this belief, was in fact an inaccurate Latin translation. Historically people in Italy ate pasta in the form of gnocchi-like dumplings – pasta fresca eaten as soon as it was prepared. It has now been asserted that the Arabs who populated Southern Italy (around the 12th Century) were the first to develop the innovation of working pasta from grain into thin long forms, capable of being dried out and stored for months or years prior to consumption. Legend has it that Cicero, the famous Roman orator was fond of "laganum", an ancient tagliatelle. The Saracens, originally from North Africa, invaded southern Italy in the 9th century and occupied Sicily for 200 hundred years. Pasta is now associated with Italians as a whole. The popularity of pasta spread to the whole of Italy after the establishment of pasta factories in the 19th century, enabling the mass production of pasta for the Italian market."

https://en.wikipedia.org/wiki/Spaghetti

The name is Italian in origin meaning a cord.

I was always told - but cannot give a source (or should it be sauce?!) - that Marco Polo brought back noodles from his trip to China. These then became Italian pasta - of which spaghetti is one of many varieties.

All agree the origins of spaghetti or pasta come from China. However, not all agree it was Marco Polo who brought it back to Europe.

http://www.whatscookingamerica.net/Pasta_Rice_Main/pasta.htm