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Cole-Hopf transformations for two and three dimensional Burgers equations with variable coefficients are reported. Like in the derivation of Cole-Hopf transformation, while changing the Burgers equation to its potential form, if we set the function of integration equal to zero, then only a specific form of Cole-Hopf transformation (CHT-1) is obtained. If we dispense with this procedure and take the function of integration into consideration then Cole-Hopf transformation is more general and it includes CHT-1 as a special case. Cole-Hopf transformations for systems which consists of the two-dimensional Burgers equation and Burgers or its potential version are also derived. Further, CHT for three-dimensional Burgers equation is stated without proof.