It is far too easy to fill the Mac menu bar with clutter. This can be a problem on modern MacBooks, which have a notch in the middle of the menu bar for the webcam—install too many apps and you'll run out of space. This, and a universal dislike of clutter, is why there are plenty of apps to clean up your menu bar out there, but those apps also can cause problems. Some apps won't launch consistently if you enable them, for one thing, and they're also yet another piece of software constantly running on your device.
A free application called Menu Bar Spacing by developer Sindre Sorhus avoids all of this by changing the spacing between menu bar icons. Even better: You don't need the application to leave the applications continuously running in order for the change to stick around—it changes the spacing at the system level, so you can launch it once and never have to open it again.
To get started, simply download and install the app. You can drag the slider to adjust the number of pixels between icons.
The change will happen instantly, though it's worth noting that all of your applications will need to quit and re-load (in theory they all re-load automatically but I had to manually restart a couple).
To be clear, you don't need this application to change the spacing between your icons—there's an obscure Terminal command you can use for the job. The application just makes things easier—you can adjust the spacing with a slider and you don't need to restart your computer in order to see the change in action. It also offers a button, to the right of the slider, that changes your menu bar back to the default spacing. It's worth keeping the application around for that alone.