What happened to the spider that bit Spiderman and gave him powers?

In the original continuity in the comics, it crawled off and died apparently. However, since that was “off camera”, it was always open to interpretation. More recently, Marvel retconned it so that the spider crawled off and bit another person, who also gained spider powers. She now goes by the name Silk. This, of course, is in the comics.

The movie continuity may be different, but it looks like they won’t be addressing Spidey’s origin in his MCU incarnation.

Maybe it got human powers?

It is living quietly in a crevace at the museum.