Spectrum sensing plays a critical role in dynamic spectrum sharing, a promising technology to address the radio spectrum shortage. In particular, sensing of Orthogonal frequency division multiplexing (OFDM) signals, a widely accepted multi-carrier transmission paradigm, has received paramount interest. Despite various efforts, most conventional OFDM sensing methods suffer from noise uncertainty, timing delay and carrier frequency offset (CFO) that significantly degrade the sensing accuracy. To address these challenges, this work develops two novel OFDM sensing frameworks drawing support from deep learning networks. Specifically, we first propose a stacked autoencoder based spectrum sensing method (SAE-SS), in which a stacked autoencoder network is designed to extract the inherent features of OFDM signals. Using these features to classify the OFDM user's activities, SAE-SS is much more robust to noise uncertainty, timing delay, and CFO than the conventional OFDM sensing methods. Moreover, SAE-SS doesn't require any prior information of signals (e.g., signal structure, pilot tones, cyclic prefix) which are essential for the conventional feature-based OFDM sensing methods. To further improve the sensing accuracy of SAE-SS, especially under low SNR conditions, we propose a stacked autoencoder based spectrum sensing method using time-frequency domain signals (SAE-TF). SAE-TF achieves higher sensing accuracy than SAW-SS at the cost of higher computational complexity. Extensive simulation results show that both SAE-SS and SAE-TF can achieve significantly higher sensing accuracy, compared with state of the art approaches that suffer from noise uncertainty, timing delay and CFO.