1. Talc
2. Gypsum
3. Calcite
4. Fluorite
5. Apatite
6. Feldspar
7. Quartz
8. Topaz
9. Corundum (ruby, sapphire)
10. Diamond
More currently common items and their relative hardness measures include:
pearl (2.5),
fingernail (2.5),
gold (2.5 to 3),
Coral: 3-4,
platinum (4 to 4.5),
a tooth (5),
opal (5.5),
lapis lazuli (5-6),
turquoise (5-6),
Glass (6-7),
peridot (6.5-7),
garnet (7 to 7.5),
and emerald (7.5-8).
Note that the scale is neither linear nor logarithmic. For example, corundum is twice as hard as topaz, but diamond is almost four times as hard as corundum.
Another way I know how hard the minerals are is because I actually cut and shape many of them myself. Using a diamond saw, the softer minerals cut like warm butter but the harder ones take effort and lots and lots of patience. Carving soapstone is child’s play compared to carving agates.
What makes minerals hard or soft? The short answer is what they are made of. The longer answer is that the molecular bonds between the atoms and the crystal structures these bonds form determine their hardness. While each mineral always has the same chemical composition (e.g. quartz is always SiO2), it can come in many different crystal structures. Carbon offers the broadest range of hardness as it comes in graphite (pencil lead that scrapes easily onto paper) and diamond. The only difference is the form of the lattices or structures that the carbon atoms form in each.
While not technically related to their hardness, friability or fragility can also be an issue to keep in mind. Druzy specimens with lots of tiny crystals could crumble if the crystals are not well attached to each other. Some crystals also have very strong cleavage plains and are susceptible to breaking along those angles. Lastly, some minerals are reactive to acids or other agents and need to be sealed or otherwise protected.