Most Lenses can change their Aperture, or their F-Stop. Most Lenses go to about f/22 or even higher. I do not usually use F-Stop over f/16. Here are my reasons.
OFF course you should always keep your Camera, and especially its’ Sensor clean. But sometimes, small Dust Particles still get into the System. At smaller F-Stops, or wider Apertures, Cameras can not focus those Particles, and you can not spot them. But at higher F-Stops, the Depth of Field gets greater, and the Particles become visible.
Another thing I just do not like and that is detrimental to Image Quality is Diffraction. Diffraction causes the Image to be generally less sharp at smaller Apertures. Find out more about Diffraction here.
Sometimes, instead of using Aperture Priority Mode, or Av, I change my Camera to Shutter Priority, or Tv. I mostly do this when I want to shoot at Night without taking a Long Exposure. And sometimes, I forget to change it back to Av from Tv. Then I shoot at 1/50 Seconds, and my Camera picks a higher F-Stop as to not overexpose the Photo. And sometimes, it turns out looking darn good.
So I guess what I am trying to say is that you should not be afraid to use those high F-Stops. Except for when your Sensor is dirty.