Modern consumer electronic devices have started executing deep learning-based intelligence services on devices, not cloud servers, to keep personal data on devices and to reduce network and cloud costs. We find such a trend as the opportunity to personalize intelligence services by updating neural networks with user data without exposing the data out of devices: on-device training. However, the limited resource of devices incurs significant difficulties. We propose a light-weight on-device training framework, NNTrainer, which provides highly memory-efficient neural network training techniques and proactive swapping based on fine-grained execution order analysis for neural networks. Moreover, its optimizations do not sacrifice the accuracy and are transparent to training algorithms; thus, prior algorithmic studies may be implemented on top of NNTrainer. The evaluations show that NNTrainer can reduce memory consumption down to 1/20 (saving 95%!) and effecttively personalizes intelligence services on devices. NNTrainer is cross-platform and practical open-source software, which is being deployed to millions of mobile devices.