Classification is one of the most important techniques to the analysis of hyperspectral remote sensing images. Nonetheless, there are many challenging problems arising in this task. Two common issues are the curse of dimensionality and the spatial information modeling. In this paper, we present a new general framework to train series of effective classifiers with spatial information for classifying hyperspectral data. The proposed framework is based on the two key observations: 1) the curse of dimensionality and the high feature-to-instance ratio can be alleviated by using random subspace (RS) ensembles; and 2) the spatial-contextual information is modeled by the extended multiattribute profiles (EMAPs). Two fast learning algorithms, i.e., decision tree (DT) and extreme learning machine (ELM), are selected as the base classifiers. Six RS ensemble methods, namely, RS with DT, random forest (RF), rotation forest, rotation RF (RoRF), RS with ELM (RSELM), and rotation subspace with ELM (RoELM), are constructed by the multiple base learners. Experimental results on both simulated and real hyperspectral data verify the effectiveness of the RS ensemble methods for the classification of both spectral and spatial information (EMAPs). On the University of Pavia Reflective Optics Spectrographic Imaging System image, our proposed approaches, i.e., both RSELM and RoELM with EMAPs, achieve the state-of-the-art performances, which demonstrates the advantage of the proposed methods. The key parameters in RS ensembles and the computational complexity are also investigated in this paper.