How to make USB devices work better on an aging desktop?

I have a 7 year old desktop computer (Dell XPS, i7-7700, 16Gb, Windows 10) which is still working very well and my preferred work computer. However when I plugged a new Logitech USB webcam into it, the picture stuttered and froze to the point that it was not usable. When I plugged a new set of USB speakers into it, the sound also broke up repeatedly and in the end they were not usable either. This makes me think there may be a problem with USB devices in general on this computer - how can I make these work better? Would it perhaps be useful to replace the USB port card?

Question by Stuart on Super User, licensed CC BY-SA. We show a short excerpt and link to the original thread as credit.