The real-world capabilities of objective speech quality measures are limited since current measures (1) are developed from simulated data that does not adequately model real environments; or they (2) predict objective scores that are not always strongly correlated with subjective ratings. Additionally, a large dataset of real-world signals with listener quality ratings does not currently exist, which would help facilitate real-world assessment. In this paper, we collect and predict the perceptual quality of real-world speech signals that are evaluated by human listeners. We first collect a large quality rating dataset by conducting crowdsourced listening studies on two real-world corpora. We further develop a novel approach that predicts human quality ratings using a pyramid bidirectional long short term memory (pBLSTM) network with an attention mechanism. The results show that the proposed model achieves statistically lower estimation errors than prior assessment approaches, where the predicted scores strongly correlate with human judgments.