Evolution by natural selection. Both Charles Darwin and Alfred Wallace came to the idea independently. Darwin had been sitting on his theory for a long time, somewhat timid to publish because it though it would be reacted to poorly, although he was slowly working on a book. However, when he caught wind that Wallace came to the same conclusion independently he panicked and rushed an abstract of his project to press, which became his most famous work, the Origin of Species.
As a way to be conciliatory, both Darwin and Wallace revealed the theory jointly in 1858, but as you probably know, Darwin gets all the credit and almost no one remembers who Alfred Wallace was.
In addition to calculus being discovered by Newton and Leibniz, logarithms were discovered independently by John Napier and Jost Burgi, and hyperbolic geometry was discovered independently by Nikolai Ivanovich Lobachevski and Janos Bolyai.
Although we often attribute sunspots to be discovered by Galileo, they were in fact seen by the naked eye perhaps as early as the 460s BC by the Greek Anaxagoras.
Furthermore, although Galileo did write three letters on sunspots which were published by the Lyncean Academy in 1613, the first published evidence of sunspots is attributed to Johannes Fabricius.
Quick list off the top of my head
Movable type - Invented by Gutenberg in Europe in ca. 1450. Invented in China in the 11th century.
Alcohol - Present in almost all historical cultures due to ease of discovery.
Jet Engines - Independently invented in both interwar Britain and Germany, with Germany creating the first practical jet fighters before the end of WWII, despite Whittle, the British inventor, developing it first.
I have to remove this as it is an overly broad topic, and we don't allow poll type questions, or "in your era" questions, which this amounts to. If you can make the question more specific, please feel free to resubmit it.