The method of random projections has become a standard tool for machine learning, data mining, and search with massive data at Web scale. The effective use of random projections requires efficient coding schemes for quantizing (real-valued) projected data into integers. In this paper, we focus on a simple 2-bit coding scheme. In particular, we develop accurate nonlinear estimators of data similarity based on the 2-bit strategy. This work will have important practical applications. For example, in the task of near neighbor search, a crucial step (often called re-ranking) is to compute or estimate data similarities once a set of candidate data points have been identified by hash table techniques. This re-ranking step can take advantage of the proposed coding scheme and estimator. As a related task, in this paper, we also study a simple uniform quantization scheme for the purpose of building hash tables with projected data. Our analysis shows that typically only a small number of bits are needed. For example, when the target similarity level is high, 2 or 3 bits might be sufficient. When the target similarity level is not so high, it is preferable to use only 1 or 2 bits. Therefore, a 2-bit scheme appears to be overall a good choice for the task of sublinear time approximate near neighbor search via hash tables. Combining these results, we conclude that 2-bit random projections should be recommended for approximate near neighbor search and similarity estimation. Extensive experimental results are provided.