To determine whether a molecule is polar or non-polar, we must consider the difference in electronegativity between the atoms and the symmetry of the molecule. Polar molecules occur when there is an electronegativity difference between the bonded atoms. Non-polar molecules either do not have any polar bonds or the polarities cancel each other out because of a symmetrical arrangement. Let's consider each molecule individually:

• HF (Hydrogen fluoride): This molecule is polar due to the high electronegativity difference between hydrogen (H) and fluorine (F).
• H₂O (Water): It is polar because of its bent shape and the difference in electronegativity between oxygen and hydrogen.
• SO₂ (Sulfur dioxide): The molecule is non-linear and has polar bonds, making it a polar molecule.
• H₂ (Hydrogen): This molecule is non-polar because it consists of two identical atoms which share electrons evenly.
• CO₂ (Carbon dioxide): Even though C=O bonds are polar, the molecule is linear and the polarities cancel out, making CO₂ non-polar.
• CH₄ (Methane): It is non-polar because the C-H bonds are evenly distributed in a tetrahedral shape, canceling out any dipole moments.
• NH₃ (Ammonia): This molecule is polar; it has a trigonal pyramidal shape with a lone pair on nitrogen, creating a dipole moment.
• HCl (Hydrogen chloride): The molecule is polar due to the electronegativity difference between hydrogen and chlorine.
• CHCl₃ (Chloroform): It has polar C-Cl bonds and is not symmetrical, resulting in a polar molecule.
• BF₃ (Boron trifluoride): This molecule is non-polar despite having polar bonds, because the shape of the molecule is trigonal planar and the dipoles cancel out.

Given this information, the non-polar molecules from the list are: $$\mathrm{H}_2, \mathrm{CO}_2, \mathrm{CH}_4, \mathrm{BF}_3$$.

Therefore, there are 4 non-polar molecules in the list given.