Measurements made on a practical system can often be subject to outliers due to sensor errors, changes in ambient environment, data loss or malicious cyber attacks. The outliers can seriously reduce the accuracy of the Kalman filter (KF) when it is applied for state estimation. This paper proposes an innovation saturation mechanism to robustify the standard KF against outliers. The basic notion is to saturate an innovation when it is distorted by an outlier, thus preventing it from impairing the state estimation process. The mechanism presents an adaptive adjustment of the saturation bound. The design is performed for both continuous- and discretetime systems, provably leading to bounded-error estimation given bounded outliers. Numerical simulation further shows the efficacy of the proposed design. Compared to many existing methods, the proposed design is computationally efficient and amenable to practical implementation, and also requires neither measurement redundancy nor extensive manual tuning.