Context: Multi-conjugate adaptive optics (MCAO) combine the advantages of both standard adaptive optics, which provide high contrast and high spatial resolution, and of wide field imaging (≈1'). Up to recently, MCAO for astronomy was limited to laboratory experiments. In this paper, we present the first scientific results obtained with the first MCAO instrument. Aims: We present a new study of the Trapezium cluster using deep MCAO images with a field of view of 1'×1' obtained at the VLT. Methods: We used deep J, H, and Ks images recently obtained with the prototype MCAO facility MAD at the VLT to search for new members and new multiple systems in the Trapezium cluster. On bright targets (Ks≈9 mag), these images allow us to reach ΔKs≈6 mag as close as 0.4 arcsec. Results: We report detection of 128 sources, including 10 new faint objects in the magnitude range between 16.1 < Ks < 17.9 mag. In addition to all previously known multiple systems with separations greater than 0.1 arcsec, we confirm the multiplicity of TCC-055. We also report the detection in J, H, and Ks of a very red extended embedded protostellar object, HC 419, previously detected only in the thermal infrared. Conclusions: Analysis of the first MCAO images obtained on the sky demonstrates not only the technical feasibility of MCAO, but also its great potential and versatility in terms of scientific output. Observations made at the ESO Paranal Observatory.