We study character-based language models in the state-of-the-art speech recognition framework. This approach has advantages over both word-based systems and so-called end-to-end ASR systems that do not have separate acoustic and language models. We describe the necessary modifications needed to build an effective character-based ASR system using the Kaldi toolkit and evaluate the models based on words, statistical morphs, and characters for both Finnish and Arabic. The morph-based models yield the best recognition results for both well-resourced and lower-resourced tasks, but the character-based models are close to their performance in the lower-resource tasks, outperforming the word-based models. Character-based models are especially good at predicting novel word forms that were not seen in the training data. Using character-based neural network language models is both computationally efficient and provides a larger gain compared to the morph and word-based systems.