After the 50 minerals meme Callan from the NOVA Geoblog is asking us what the 5 most important mineral are if we had to explain to a non-geologist.
Quartz: Many others already mentioned it. It is one of the toughest and most widespread minerals that everyone will get in touch with sooner or later. Also it is a major building stone of the continental crust and makes for nice juwelery in the form of amethyst, rock crystals and smokey quartz. Last but not least it is part of not just a lot of sedimentary rocks but also part of every computer or optical device in the form of silicium.
Feldspar: Is actually a group of silicate minerals, however most non-geo-educated people won't be able to seperate them anyways. Furthermore, they also compromise a large portion of the earths crust and are highly useful as a resource for ceramics, pottery (clay minerals also play a role here) and construction materials.
Calcite/Aragonite: Anyone taking a vacation in warmer climate will come across carbonate producing organisms like corals, crinoids, mussels and many others. Everyone likely heard of the Great Barrier reef or the Carrara marble. It can host great fossils and is widespread in many areas of the world. Also it is relatively easy to recognise. Last but not least it is a very important resource for a variety of economical activites like cement production, paints, filling material, glass and ceramics.
Olivine: Mentioned by Silver Fox it constitutes a major portion of the earth's mantle. One may find it in basalts which is what most people know. It can be beautifully green and of "gemstone quality". Olivine rich rocks are hosts to important ore deposits, i.e. chromium.
Chalcosine/Chalcopyrite: Actually two different minerals but together the most important source of copper. After silver copper is the best electrical conductor and thus one of the most important metals in our society. Any electrical device needs copper. Additionally, together with tin it forms a very important alloy: Bronze.