Our computers use quantum effects every day – silicon chips rely on quantum physics to work because quantum physics tell us how electrons behave in solids. Light is a very quantum object – when it goes through a prism and the colours split, that’s light acting like a wave, which to me is a very quantum effect (although we understood how light works hundreds of years ago).
Lasers are based on the fact that light is photons, and on the quantised energy levels of atoms (which means that they always shoot out the same types of photons). We all have lasers of some sort in our homes, like in the PS3, in a blue ray player, or in a dvd player. Plus, lasers are used all the time in things like manufacturing, so lots of stuff you own only exists because of lasers.
There is an experiment in Physics that uses a beam of electrons to cause an interference pattern using the double slit experiment (diffraction). For electrons to interfere with one another and cause constructive and destructive interference as they do, the electrons must behave like waves. Experimentalists then tried the double slit experiment firing one electron at a time through the slits. The single electrons still produced an interference pattern, meaning that the electron must have gone through both slits at the same time and interfered with itself. This is an example of a quantum effect you can “see”.
You can perform that double slit experiment for yourself by creating a wave in water and passing it through two slits. You will see an fringe pattern where the two wave interfere constructively giving you 1 wave where you’d expect to see 2.