The deep understanding of online users on the basis of their behavior data is critical to providing personalized services to them. However, the existing methods for learning user representations are usually based on supervised frameworks such as demographic prediction and product recommendation. In addition, these methods highly rely on labeled data to learn user-representation models, and the user representations learned using these methods can only be used in specific tasks. Motivated by the success of pretrained word embeddings in many natural language processing (NLP) tasks, we propose a simple but effective neural user-embedding approach to learn the deep representations of online users by using their unlabeled behavior data. Once the users are encoded to low-dimensional dense embedding vectors, these hidden user vectors can be used as additional user features in various user-involved tasks, such as demographic prediction, to enrich user representation. In our neural user embedding (NEU) approach, the behavior events are represented in two ways. The first one is the ID-based event embedding, which is based on the IDs of these events, and the second one is the text-based event embedding, which is based on the textual content of these events. Furthermore, we conduct experiments on a real-world web browsing dataset. The results show that our approach can learn informative user embeddings by using the unlabeled browsing-behavior data and that these user embeddings can facilitate many tasks that involve user modeling such as user-age prediction and -gender prediction.