Let us examine the structure and bonding in each molecule:

• $\text{CO}_2$: The carbon atom forms two double bonds with two oxygen atoms ($\text{O=C=O}$). Each double bond consists of one $\sigma$ bond and one $\pi$ bond. Thus, $\text{CO}_2$ contains 2 $\pi$ bonds.
• $\text{H}_2\text{O}$: The central oxygen atom is $sp^3$ hybridised and forms two single bonds ($\sigma$ bonds) with two hydrogen atoms. The remaining valence electrons form two lone pairs. There are no $\pi$ bonds in water.
• $\text{SO}_2$: The central sulphur atom forms one double bond and one single bond with oxygen atoms (in its resonance structures). Thus, it contains $\pi$ bonding.
• $\text{NO}_2$: The central nitrogen atom forms one double bond and one single bond with oxygen atoms, containing a $\pi$ bond. Therefore, $\text{H}_2\text{O}$ is the only molecule among the options that contains no $\pi$-bond.