Fetal brain extraction is a necessary first step in most computational fetal brain MRI pipelines. However, it has been a very challenging task due to non-standard fetal head pose, fetal movements during examination, and vastly heterogeneous appearance of the developing fetal brain and the neighboring fetal and maternal anatomy across various sequences and scanning conditions. Development of a machine learning method to effectively address this task requires a large and rich labeled dataset that has not been previously available. As a result, there is currently no method for accurate fetal brain extraction on various fetal MRI sequences. In this work, we first built a large annotated dataset of approximately 72,000 2D fetal brain MRI images. Our dataset covers the three common MRI sequences including T2-weighted, diffusion-weighted, and functional MRI acquired with different scanners. Moreover, it includes normal and pathological brains. Using this dataset, we developed and validated deep learning methods, by exploiting the power of the U-Net style architectures, the attention mechanism, multi-contrast feature learning, and data augmentation for fast, accurate, and generalizable automatic fetal brain extraction. Our approach leverages the rich information from multi-contrast (multi-sequence) fetal MRI data, enabling precise delineation of the fetal brain structures. Evaluations on independent test data show that our method achieves accurate brain extraction on heterogeneous test data acquired with different scanners, on pathological brains, and at various gestational stages. This robustness underscores the potential utility of our deep learning model for fetal brain imaging and image analysis.