Open-domain neural dialogue models have achieved high performance in response ranking and evaluation tasks. These tasks are formulated as a binary classification of responses given in a dialogue context, and models generally learn to make predictions based on context-response content similarity. However, over-reliance on content similarity makes the models less sensitive to the presence of inconsistencies, incorrect time expressions and other factors important for response appropriateness and coherence. We propose approaches for automatically creating adversarial negative training data to help ranking and evaluation models learn features beyond content similarity. We propose mask-and-fill and keyword-guided approaches that generate negative examples for training more robust dialogue systems. These generated adversarial responses have high content similarity with the contexts but are either incoherent, inappropriate or not fluent. Our approaches are fully data-driven and can be easily incorporated in existing models and datasets. Experiments on classification, ranking and evaluation tasks across multiple datasets demonstrate that our approaches outperform strong baselines in providing informative negative examples for training dialogue systems.