Why is density of chloroform greater than water?
The density of a substance depends on its molecular density and packing fraction (where you need to be consistent in definiting the molar volume in calculating both attributes).
However you are looking for a simpler explanation that gets the general trends right.   Just looking at molecular mass is too simple—larger molecules have greater mass, but take up more space.  So what would be a simple model that works reasonably well?
I suspect the main determinant of density is the average mass of a molecule's atoms, and that relative atomic sizes, as well as packing density, while important, are secondary contributors.
Given this, let's construct our very rough model for predicting relative densities by comparing just the average atomic masses of the molecule's atoms, and see if that, by itself, can explain most of the trends.
Of course, since we are ignoring these other factors, our simple model is imperfect and thus, as expected, will have many exceptions (one of which is included, and bolded, below). Nevertheless, in spite of the very simple nature of this model, it does surprisingly well in matching the general trends (at least for the substances shown here).
In each case I have calculated the average atomic mass of the atoms (u/atom) from $\frac{\text{molecular mass}}{\text{no. of atoms}}$:
Hexane ($\ce{C6H14}$): 86.18/20 = 4.3 u/atom; density = 0.661 g/$\text{cm}^3$
Octane ($\ce{C8H18}$): 114.23/26 = 4.4 u/atom; density = 0.703 g/$\text{cm}^3$
Water ($\ce{H2O}$):  18.015/3 = 6.0 u/atom; density = 0.997 g/$\text{cm}^3$ (at 25$^\circ$C)
Methyl chloride ($\ce{CH3Cl}$):  50.485/5 = 10.1 u/atom; density = 0.911 g/$\textbf{cm}^{\bf{3}}$   (note the exception to the trend; it works well in comparing like compounds—this one vs. the ones below—but fails when comparing very unlike compounds—this one vs. water—when the average atomic masses of the atoms are too close)
Methylene chloride ($\ce{CH2Cl2})$: 84.927/5 = 17.0 u/atom; density = 1.325 g/$\text{cm}^3$
Chloroform ($\ce{CHCl3})$: 119.369/5 = 23.9 u/atom; density = 1.492 g/$\text{cm}^3$
Carbon tetrachloride ($\ce{CCl4}$): 153.8118/5 = 30.8 u/atom; density = 1.594 g/$\text{cm}^3$
Carbon tetrabromide ($\ce{CBr4}$): 331.627/5 = 66.3 u/atom; density = 3.42 g/$\text{cm}^3$ (m.p. = 89$^\circ$C, so it's solid at room temperature)
Carbon tetraiodide ($\ce{CI4}$): 519.628/5 = 103.9 u/atom; density = 6.36 g/$\text{cm}^3$ (m.p. = 168$^\circ$C, so it's solid at room temperature)
Mercury ($\ce{Hg}$): 200.592/1 = 200.6 u/atom; density = 13.534 g/$\text{cm}^3$