Drug-Target binding Affinity (DTA) prediction is essential for drug discovery. Despite the application of deep learning methods to DTA prediction, the achieved accuracy remain suboptimal. In this work, inspired by the recent success of retrieval methods, we propose $k$NN-DTA, a non-parametric embedding-based retrieval method adopted on a pre-trained DTA prediction model, which can extend the power of the DTA model with no or negligible cost. Different from existing methods, we introduce two neighbor aggregation ways from both embedding space and label space that are integrated into a unified framework. Specifically, we propose a \emph{label aggregation} with \emph{pair-wise retrieval} and a \emph{representation aggregation} with \emph{point-wise retrieval} of the nearest neighbors. This method executes in the inference phase and can efficiently boost the DTA prediction performance with no training cost. In addition, we propose an extension, Ada-$k$NN-DTA, an instance-wise and adaptive aggregation with lightweight learning. Results on four benchmark datasets show that $k$NN-DTA brings significant improvements, outperforming previous state-of-the-art (SOTA) results, e.g, on BindingDB IC$_{50}$ and $K_i$ testbeds, $k$NN-DTA obtains new records of RMSE $\bf{0.684}$ and $\bf{0.750}$. The extended Ada-$k$NN-DTA further improves the performance to be $\bf{0.675}$ and $\bf{0.735}$ RMSE. These results strongly prove the effectiveness of our method. Results in other settings and comprehensive studies/analyses also show the great potential of our $k$NN-DTA approach.