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:
$$ \begin{align} \ce{HCl + H2O &<=> Cl- + H3O+}\\ \ce{HNO3 + H2O &<=> NO3- + H3O+}\\ \ce{CH3-COOH + H2O &<=> CH3-COO+ + H3O+}\\ \ce{HCOOH + H2O &<=> HCOO- + H3O+}\\ \ce{HCl + NaOH &<=> NaCl + H2O} \end{align} $$$$ \begin{align} \ce{HCl + H2O &<=> Cl- + H3O+}\\ \ce{HNO3 + H2O &<=> NO3- + H3O+}\\ \ce{CH3-COOH + H2O &<=> CH3-COO- + H3O+}\\ \ce{HCOOH + H2O &<=> HCOO- + H3O+}\\ \ce{HCl + NaOH &<=> NaCl + H2O} \end{align} $$