This paper investigates the robustness of NLP against perturbed word forms. While neural approaches can achieve (almost) human-like accuracy for certain tasks and conditions, they often are sensitive to small changes in the input such as non-canonical input (e.g., typos). Yet both stability and robustness are desired properties in applications involving user-generated content, and the more as humans easily cope with such noisy or adversary conditions. In this paper, we study the impact of noisy input. We consider different noise distributions (one type of noise, combination of noise types) and mismatched noise distributions for training and testing. Moreover, we empirically evaluate the robustness of different models (convolutional neural networks, recurrent neural networks, non-neural models), different basic units (characters, byte pair encoding units), and different NLP tasks (morphological tagging, machine translation).