It has always been a known fact that Spider-Man could never communicate. He had no such powers initially. However, it has been a shock to see that in many of the past storylines he could communicate with the spiders. The Marvel Universe only includes a few characters that do have the power to communicate with the creatures. Some characters included had the ability to communicate.
The Handsome spiderman!!!
The Spider-Man did not receive his powers right from the beginning. However, he slowly and steadily learned various abilities which included climbing, clinging and few other human powers. He did not have the power to communicate with others. However, he seems to have now gained that power. Spider-Man also experienced a near-fatal death which was arranged by Morlun, his biggest villain. However, it was his cocoon that acted as a shield for him.
Do not mess with me, Spider-Man!
After getting his life back because of the cocoon, he was then blessed with the power to communicate with the other spiders. It was also seen that Spider-Man was seen confronting the Doctor to let him communicate to a Spider. This incident was a part of the mini-story Doctor Strange #390.
Let me fly high!!!
However, is that even still a power remains a rather big question. If it is then that is the most powerful thing for any spider to possess. As of now, Ant-man is the only spider that had the ability to communicate with other spiders.