Many state-of-the-art neural models for NLP are heavily parameterized and thus memory inefficient. This paper proposes a series of lightweight and memory efficient neural architectures for a potpourri of natural language processing (NLP) tasks. To this end, our models exploit computation using Quaternion algebra and hypercomplex spaces, enabling not only expressive inter-component interactions but also significantly ($75\%$) reduced parameter size due to lesser degrees of freedom in the Hamilton product. We propose Quaternion variants of models, giving rise to new architectures such as the Quaternion attention Model and Quaternion Transformer. Extensive experiments on a battery of NLP tasks demonstrates the utility of proposed Quaternion-inspired models, enabling up to $75\%$ reduction in parameter size without significant loss in performance.