Do non-redox reactions exist? Redox reaction is a type of chemical reaction, and is the result of electron transfer between chemical species. But, all chemical reactions somehow involve electron transfer!

So, are there chemical reactions without electron transfer?
There are many, here are some examples


Ion interchange reactions of various types, such as precipitation

$\ce{NaCl + AgNO3 -&gt; AgCl \downarrow + NaNO3 }$
Polar molecule insert/ejection. The most common case is hydrolysis and reverse reactions.

$\ce{PCl5 + 4 H2O -&gt;  H3PO4 + 5 HCl}$
Reorganization of bonds between atoms of same type, such as catalytic benzene synthesis from acetylene 

$\ce{3 C2H2 -&gt; C6H6}$
Ligand exchange

$\ce{ [Fe(H2O)6]^{3+} + 6CN- -&gt; [Fe(CN)6]^{3-} + 6 H2O}$
polar oligomerization

$\ce{ H2O + n CH2O -&gt; HO-(-CH2-O-)_{n}-H}$