We present the latest developments of the MadGraph/MadEvent Monte Carlo event generator and several applications to hadron collider physics. In the current version events at the parton, hadron and detector level can be generated directly from a web interface, for arbitrary processes in the Standard Model and in several physics scenarios beyond it (HEFT, MSSM, 2HDM). The most important additions are: a new framework for implementing user-defined new physics models; a standalone running mode for creating and testing matrix elements; generation of events corresponding to different processes, such as signal(s) and backgrounds, in the same run; two platforms for data analysis, where events are accessible at the parton, hadron and detector level; and the generation of inclusive multi-jet samples by combining parton-level events with parton showers. To illustrate the new capabilities of the package some applications to hadron collider physics are presented: I. Higgs search in pp → H → W+W-: signal and backgrounds. II. Higgs CP properties: pp → Hjj in the HEFT. III. Spin of a new resonance from lepton angular distributions. IV. Single-top and Higgs associated production in a generic 2HDM. V. Comparison of strong SUSY pair production at the SPS points. VI. Inclusive W+jets matched samples: comparison with Tevatron data.