The highest dipole moment is for:

The molecules $\text{CH}_4$ and $\text{CCl}_4$ have highly symmetrical tetrahedral geometries, resulting in a net dipole moment of zero.

For $\text{CH}_2\text{Cl}_2$ and $\text{CHCl}_3$, the net dipole moment is the vector sum of the individual C-H and C-Cl bond dipoles. In $\text{CH}_2\text{Cl}_2$, the resultant of the two C-Cl bond dipoles and the two C-H bond dipoles reinforce each other more effectively than the bond dipoles in $\text{CHCl}_3$.

The experimental dipole moments are:
$\text{CH}_4 = 0 \text{ D}$
$\text{CCl}_4 = 0 \text{ D}$
$\text{CHCl}_3 = 1.04 \text{ D}$
$\text{CH}_2\text{Cl}_2 = 1.60 \text{ D}$

Thus, $\text{CH}_2\text{Cl}_2$ has the highest dipole moment among the given options.

Answer: $\text{CH}_2\text{Cl}_2$