ADB device stuck in "connecting" state

A friend told me to try to swap ports to a USB 2.0 instead of USB 3.0. After doing so it worked instantly as expected.

[EDIT] It appears that this has more to do with the capabilities of the motherboard than the version of USB the port is. The opposite might be true for you, or just any other port.

I had the same problem and found that the issue was solved by switching off USB debugging on the device, then switching it on again.