Proton NMR chemical shift of water peak in different solvents
Consider also water in addition to the solvents you mention:


water-d2 (or, $\ce{D2O}$) is an extensively H-bonding polar solvent (dielectric constant $\epsilon = 79$) 
$\ce{DMSO-d6}$) is polar ($\epsilon= 47$) but aprotic (no-H-bond donation ability)
chloroform-d is an apolar aprotic solvent ($\epsilon=4.81$)


Now consider the state of a trace amount of $\ce{H2O}$ in each of these solvents, giving rise to an NMR signal: 


in $\ce{D2O}$ the trace $\ce{H}$ can exchange and forms $\ce{HDO}$ which retains an extensive H-bond network. $\ce{H}$ is strongly deshielded by bonded and H-bonded electronegative oxygen and due to the formation of oxonium ion with $\ce{H}$ carrying a significant positive partial charge. The chemical shift is $\approx \pu{4.7 ppm}$  
in DMSO-d6, $\ce{H}$ is strongly coordinated (H-bonded) by DMSO oxygen atoms, resulting in substantial shielding. The chemical shift is $\approx \pu{3.33 ppm}$
in chloroform-d interactions with the solvent are comparably weak and mainly dipolar or dispersion interactions. $\ce{H}$ experiences deshielding mainly due to directly bonded oxygen. The chemical shift is $\approx \pu{1.56 ppm}$


The following table shows shifts for residual water $\ce{H}$ in different solvents ([1]; dielectric constants are for non-deuterated solvents):

$\begin{array}{c}
\begin{array}{c|c|c}
\text{solvent} &amp;\text{shift(ppm)}&amp;\epsilon\\\hline
\ce{C6D6 }&amp;0.40 &amp; 2.28\\
\text{toluene-d8} &amp;0.43 &amp;2.38\\
\ce{C6D5Cl} &amp;1.03 &amp;5.69\\
\ce{CD2Cl2 }&amp;1.52 &amp;9.08\\
\ce{CDCl3} &amp;1.56 &amp;4.81\\
\ce{CD3CN}  &amp;2.13 &amp;36.64\\
\text{THF-d8} &amp;2.46 &amp;7.52\\
 \ce{(CD3)2CO} &amp;2.84 &amp;21.01\\
 \ce{(CD3)2SO}  &amp;3.33 &amp;47\\
\text{TFE-d3} &amp;3.66&amp;8.55 \\
\ce{CD3OD} &amp;4.87 &amp;32.6\\
\end{array}
\end{array}$

Note that the most deshielding solvents are the protic H-bonding ones (the bottom two). 
Next in effectiveness are those with oxygen atoms with lone electron pairs available for H-bonding.
Note also that the top three have an additional effect on water shifts due to the aromatic ring current.



Reference
[1] Fulmer et al. Organometallics 2010, 29, 2176–2179