We implement a search for exoplanets in campaigns zero through eight (C0-8) of the K2 extension of the Kepler spacecraft. We apply a modified version of the Quasi-periodic Automated Transit Search (QATS) planet search algorithm to K2 light curves produced by the EVEREST pipeline, carrying out the C0-8 search on 1.5x10^5^ target stars with magnitudes in the range of Kp=9-15. We detect 818 transiting planet candidates, of which 374 were undiscovered by prior searches, with {64, 15, 5, 2, 1} in {2, 3, 4, 5, 6}-planet multiplanet candidate systems, respectively. Of the new planets detected, 100 orbit M dwarfs, including one that is potentially rocky and in the habitable zone. A total of 154 of our candidates reciprocally transit with our solar system: they are geometrically aligned to see at least one solar system planet transit. We find candidates that display transit timing variations and dozens of candidates on both period extremes with single transits or ultrashort periods. We point to evidence that our candidates display similar patterns in frequency and size-period relation to confirmed planets, such as tentative evidence for the radius gap. Confirmation of these planet candidates with follow-up studies will increase the number of K2 planets by up to 50%, and characterization of their host stars will improve statistical studies of planet properties. Our sample includes many planets orbiting bright stars amenable for radial velocity follow-up and future characterization with JWST. We also list the 579 eclipsing binary systems detected as part of this search.