We present the results of a search for potential transit signals in the first three years of photometry data acquired by the Kepler mission. The targets of the search include 112,321 targets that were observed over the full interval and an additional 79,992 targets that were observed for a subset of the full interval. From this set of targets we find a total of 11,087 targets that contain at least one signal that meets the Kepler detection criteria: periodicity of the signal, an acceptable signal-to-noise ratio, and three tests that reject false positives. Each target containing at least one detected signal is then searched repeatedly for additional signals, which represent multi-planet systems of transiting planets. When targets with multiple detections are considered, a total of 18,406 potential transiting planet signals are found in the Kepler mission data set. The detected signals are dominated by events with relatively low signal-to-noise ratios and by events with relatively short periods. The distribution of estimated transit depths appears to peak in the range between 20 and 30 parts per million, with a few detections down to fewer than 10 parts per million. The detections exhibit signal-to-noise ratios from 7.1σ, which is the lower cutoff for detections, to over 10,000σ, and periods ranging from 0.5 days, which is the shortest period searched, to 525 days, which is the upper limit of achievable periods given the length of the data set and the requirement that all detections include at least three transits. The detected signals are compared to a set of known transit events in the Kepler field of view, many of which were identified by alternative methods; the comparison shows that the current search recovery rate for targets with known transit events is 98.3%.