For bounded-length sequences of small alphabet sizes (e.g. digits 0-9 only), it's possible to use a convolutional neural network to get human-level 98+% accuracy (see Google's street view house numbers paper).
Even for general purpose OCR, I personally built an OCR engine from scratch in 2013 using convolutional neural networks and cuDNN that readily beat Tesseract and was competitive with ABBYY (both use ad hoc methods). Character-level segmentation and classification (with distractors) can get you pretty far with enough training data.
It did take me 6 months of time though, and I had some help along the way...