I find it very interesting that Alexander the Great, like Ghengis Khan, managed to conquer so much. I've also been reading up on the history of areas like Afghanistan and the surrounding areas. In the places that he conquered, is there anything there that remains today, be it a cultural aspect like a tradition, borrowed words used in the language, or archaeological sites?
Not to discourage any further answers, but there are numerous excellent posts about the successor states which split off from Alexander's empire after his death. In the beginning, these states were ruled by generals of Alexander and had an influx Greek immigration. As such, they are interesting examples of how Greek culture mixed with other cultures after Alex the G's conquests.
This is part of the reason why Greek was the lingua franca of the ancient world until the Middle Ages. Even at the height of the Roman Empire, Greek was more widely spoken than Latin in the eastern Mediterranean. That wouldn't have been true without Alexander.
Three very interesting examples of these empires are Seleucid Empire in Persia and the Levant, the Ptolemaic Kingdom in Egypt, and the Greco-Bactrian Kingdom in modern Afghanistan.
/u/Daeres described the rise and fall of the Seleucid Empire in this answer. The Seleucid Empire was the largest and greatest of the successor states, and was founded by Seleucus I, Alexander's general and bodyguard. Since it was mostly comprised of the former Persian Empire, it contained numerous cultures, languages and kingdoms. The Greek Seleucid dynasty also founded new cities in their empire.
Daeres also gave an interesting answer on the Greco-Bactrian kingdom and it's ultimate fate. In another answer Daeres explained the term "Hellenization", which referred to both the time period after Alexander and the process by which Greek culture spread and diffused in the ancient world.
FAQ on the Ptolemaic Egyptian empire with answers by /u/cleopatra_philopater
Why the Seleucid Empire is so underappreciated by /u/Iphikrates
The long and the short of it is that Alexander the Great permanently impacted the cultures and history of the Near East, Mediterranean and North Africa.