Context. The X-ray emission from flares on cool (i.e. spectral-type F-M) stars is indicative of very energetic, transient phenomena, associated with energy release via magnetic reconnection. Aims. We present a uniform, large-scale survey of X-ray flare emission. The XMM-Newton Serendipitous Source Catalogue and its associated data products provide an excellent basis for a comprehensive and sensitive survey of stellar flares -both from targeted active stars and from those observed serendipitously in the half-degree diameter field-of-view of each observation. Methods. The 2XMM Catalogue and the associated time-series ("light-curve") data products have been used as the basis for a survey of X-ray flares from cool stars in the Hipparcos-Tycho-2 catalogue. In addition, we have generated and analysed spectrally-resolved (i.e. hardness-ratio), X-ray light-curves. Where available, we have compared XMM OM UV/optical data with the X-ray light-curves. Results. Our sample contains ∼130 flares with well-observed profiles; they originate from ∼70 stars. The flares range in duration from ∼10 3 to ∼10 4 s, have peak X-ray fluxes from ∼10 −13 to ∼10 −11 erg cm −2 s −1 , peak X-ray luminosities from ∼10 29 to ∼10 32 erg s −1 , and X-ray energy output from ∼10 32 to ∼10 35 erg. Most of the ∼30 serendipitously-observed stars have little previously reported information. The hardness-ratio plots clearly illustrate the spectral (and hence inferred temperature) variations characteristic of many flares, and provide an easily accessible overview of the data. We present flare frequency distributions from both target and serendipitous observations. The latter provide an unbiased (with respect to stellar activity) study of flare energetics; in addition, they allow us to predict numbers of stellar flares that may be detected in future X-ray wide-field surveys. The serendipitous sample demonstrates the need for care when calculating flaring rates, especially when normalising the number of flares to a total exposure time, where it is important to consider both the stars seen to flare and those from which variability was not detected (i.e. measured as non-variable), since in our survey, the latter outnumber the former by more than a factor ten. The serendipitous variable and "non-variable" stars appear very similar in terms of the distributions of general properties such as quiescent X-ray luminosity; from the available data, it is unclear whether the distinction by flaring is due to an additional, intrinsic property such as intra-system interactions in a close binary system, or is simply the result of limited observations and detection thresholds on a random flaring process, with no real difference between the two samples, or may be a combination of these effects. However, the number of detected flares compared with the number of stars not seen to vary is broadly consistent with estimates based on Poisson statistics.