We study numerically two-dimensional nanoparticles with a non-regular shape and demonstrate that these particles can support many more plasmon resonances than a particle with a regular shape (e.g. an ellipse). The electric field distributions associated with these different resonances are investigated in detail in the context of near-field microscopy. Depending on the particle shape, extremely strong and localized near-fields, with intensity larger than 10(5) that of the illumination wave, can be generated. We also discuss the spectral dependence of these near-fields and show that different spatial distributions are observed, depending which plasmon resonance is excited in the particle.