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?
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
$\ce{NaCl + AgNO3 -> AgCl \downarrow + NaNO3 }$
Polar molecule insert/ejection. The most common case is hydrolysis and reverse reactions.
$\ce{PCl5 + 4 H2O -> H3PO4 + 5 HCl}$
Reorganization of bonds between atoms of same type, such as catalytic benzene synthesis from acetylene
$\ce{3 C2H2 -> C6H6}$
Ligand exchange
$\ce{ [Fe(H2O)6]^{3+} + 6CN- -> [Fe(CN)6]^{3-} + 6 H2O}$
polar oligomerization
$\ce{ H2O + n CH2O -> HO-(-CH2-O-)_{n}-H}$
Yes, there are precipitation reactions (which don't have electron transfer), e.g. silver cation and chloride anion combining to make silver chloride, a slightly soluble compound. Also barium sulfate will precipitate.
Hydrolysis of polysaccharides and proteins: with the assistance of enzymes, water is use to break up polysaccharides into simple sugars.
There are others.
Of course there are non-redox reactions, for example, acid-base reactions. They do not involve any electron transfer only protons move around (so no oxidation numbers change). Here are some basic examples:
$$ \begin{align} \ce{HCl + H2O &<=> Cl- + H3O+}\\ \ce{HNO3 + H2O &<=> NO3- + H3O+}\\ \ce{CH3-COOH + H2O &<=> CH3-COO- + H3O+}\\ \ce{HCOOH + H2O &<=> HCOO- + H3O+}\\ \ce{HCl + NaOH &<=> NaCl + H2O} \end{align} $$
For us to understand the redox nature of the above examples, we have to use the definition of redox as gain or loss of electron density, not just electrons. For instance, in the reaction between sodium hydroxide and hydrochloric acid to give sodium chloride and water, chlorine is reduced by gaining electron density in its bond with sodium compared to its bond with hydrogen. Why? Because sodium releases electron with more ease than hydrogen. Consequently, chlorine binds the electron more tightly thereby creating higher electron density. This principle applies to all chemical reactions and is the result of the concept of electronegativity. It is very important in biochemical reactions. I have also seen its importance in the molecular basis of all diseases, which are as a matter of fact the result of oxidation reactions in the body.