In this paper, we propose a novel feedforward adaptive quantization scheme called the sample-adaptive product quantizer (SAPQ). This is a structurally constrained vector quantizer that uses unions of product codebooks. SAPQ is based on a concept of adaptive quantization to the varying samples of the source and is very different from traditional adaptation techniques for nonstationary sources. SAPQ quantizes each source sample using a sequence of quantizers. Even when using scalar quantization in SAPQ, we can achieve performance comparable to vector quantization (with the complexity still close to that of scalar quantization). We also show that important lattice-based vector quantizers can be constructed using scalar quantization in SAPQ. We mathematically analyze SAPQ and propose a algorithm to implement it. We numerically study SAPQ for independent and identically distributed Gaussian and Laplacian sources. Through our numerical study, we find that SAPQ using scalar quantizers achieves typical gains of 13 dB in distortion over the Lloyd-Max quantizer. We also show that SAPQ can he used in conjunction with vector quantizers to further improve the gains.