Scaling existing applications and solutions to multiple human languages has traditionally proven to be difficult, mainly due to the language-dependent nature of preprocessing and feature engineering techniques employed in traditional approaches. In this work, we empirically investigate the factors affecting language-independent models built with multilingual representations, including task type, language set and data resource. On two most representative Natural Language Processing tasks - sentence classification and sequence labeling, we show that language-independent models can be comparable to or even outperforms the models trained using monolingual data, and they are generally more effective on sentence classification. We experiment language-independent models with many different languages and show that they are more suitable for typologically similar languages. We also explore the effects of different data sizes when training and testing language-independent models, and demonstrate that they are not only suitable for high-resource languages, but also very effective in low-resource languages.