Pre-main sequence (PMS) stars are known to produce powerful X-ray flares which resemble magnetic reconnection solar flares scaled by factors up to 10^4. However, numerous puzzles are present including the structure of X-ray emitting coronae and magnetospheres, effects of protoplanetary disks, and effects of stellar rotation. To investigate these issues in detail, we examine 216 of the brightest flares from 161 PMS stars observed in the Chandra Orion Ultradeep Project (COUP). These constitute the largest homogeneous dataset of PMS, or indeed stellar flares at any stellar age, ever acquired. Our effort is based on a new flare spectral analysis technique that avoids nonlinear parametric modeling. It can be applied to much weaker flares and is more sensitive than standard methods. We provide a catalog with >30 derived flare properties and an electronic atlas for this unique collection of stellar X-ray flares. The current study (Paper I) examines the flare morphologies, and provides general comparison of COUP flare characteristics with those of other active X-ray stars and the Sun. Paper II will concentrate on relationships between flare behavior, protoplanetary disks, and other stellar properties. Several results are obtained. First, the COUP flares studied here are among the most powerful, longest, and hottest stellar X-ray flares ever studied. Second, no significant statistical differences in peak flare luminosity or temperature distributions are found among different morphological flare classes, suggesting a common underlying mechanism for all flares. Third, comparison with the general solar-scaling laws indicates that COUP flares may not fit adequately proposed power-temperature and duration-temperature solar-stellar fits. Fourth, COUP super-hot flares are found to be brighter but shorter than ... ABRIDGED

Accepted for publication in ApJ (07/11/08); 63 pages, 16 figures, 4 tables