Experienced pipeline operators utilize Magnetic Flux Leakage (MFL) sensors to probe oil and gas pipelines for the purpose of localizing and sizing different defect types. A large number of sensors is usually used to cover the targeted pipelines. The sensors are equally distributed around the circumference of the pipeline, and every three millimeters the sensors measure MFL signals. Thus, the collected raw data is so big that it makes the pipeline probing process difficult, exhausting and error-prone. Machine learning approaches such as neural networks have made it possible to effectively manage the complexity pertaining to big data and learn their intrinsic properties. We concentrate, in this work, on the applicability of artificial neural networks in defect depth estimation and present a detailed study of various network architectures. Discriminant features, which characterize different defect depth patterns, are first obtained from the raw data. Neural networks are then trained using these features. The Levenberg-Marquardt back-propagation learning algorithm is adopted in the training process, during which the weight and bias parameters of the networks are tuned to optimize their performances. Compared with the performance of pipeline inspection techniques reported by service providers such as GE and ROSEN, the results obtained using the method we proposed are promising. For instance, within ±10% error-tolerance range, the proposed approach yields an estimation accuracy at 86%, compared to only 80% reported by GE, and within ±15% error-tolerance range, it yields an estimation accuracy at 89% compared to 80% reported by ROSEN.