We present the results from the first two years of the Planet Hunters Next Generation Transit Survey (NGTS) citizen science project, which searches for transiting planet candidates in data from the NGTS by enlisting the help of members of the general public. Over 8000 registered volunteers reviewed 138,198 light curves from the NGTS Public Data Releases 1 and 2. We utilize a user weighting scheme to combine the classifications of multiple users to identify the most promising planet candidates not initially discovered by the NGTS team. We highlight the five most interesting planet candidates detected through this search, which are all candidate short-period giant planets. This includes the TIC-165227846 system that, if confirmed, would be the lowest-mass star to host a close-in giant planet. We assess the detection efficiency of the project by determining the number of confirmed planets from the NASA Exoplanet Archive and TESS Objects of Interest (TOIs) successfully recovered by this search and find that 74% of confirmed planets and 63% of TOIs detected by NGTS are recovered by the Planet Hunters NGTS project. The identification of new planet candidates shows that the citizen science approach can provide a complementary method to the detection of exoplanets with ground-based surveys such as NGTS.