Inter-subject variabilities in brain signals can significantly deteriorate the accuracy of brain-computer interface (BCI) systems. Every subject has different brain signals; also, the performance of a subject varies widely between sessions, within a session, between on-line and off-line settings, and even from epoch to epoch. Such variabilities arise in measurements obtained during different BCI sessions require subject and session specific decoder models. This work proposes three different deep learning models for subject-independent decoding of event-related potentials in electroencephalographic signals: 1) shallow convolutional neural network, 2) gated recurrent neural network, and 3) CNN-RNN-Net: a hybrid one-dimensional convolution and a gated recurrent unit model. Experimental results demonstrate that the proposed models outperform the conventional baseline models in decoding subject-independent data. Moreover, among the three models, the CNN-RNN-Net has shown improved classification results.