Context. The Kepler K2 mission now makes it possible to find and study a wider variety of eclipsing binary stars than has been possible to-date, particularly long-period systems with narrow eclipses. Aims. Our aim is to characterise eclipsing binary stars observed by the Kepler K2 mission with orbital periods longer than P ≈ 5.5 days. Methods. The ellc binary star model has been used to determine the geometry of eclipsing binary systems in Kepler K2 campaigns 1, 2 and 3. The nature of the stars in each binary is estimated by comparison to stellar evolution tracks in the effective temperature – mean stellar density plane. Results. 43 eclipsing binary systems have been identified and 40 of these are characterised in some detail. The majority of these systems are found to be late-type dwarf and sub-giant stars with masses in the range 0.6–1.4 solar masses. We identify two eclipsing binaries containing red giant stars, including one bright system with total eclipses that is ideal for detailed follow-up observations. The bright B3V-type star HD 142883 is found to be an eclipsing binary in a triple star system. We observe a series of frequencies at large multiples of the orbital frequency in BW Aqr that we tentatively identify as tidally induced pulsations in this well-studied eccentric binary system. We find that the faint eclipsing binary EPIC 201160323 shows rapid apsidal motion. Rotational modulation signals are observed in 13 eclipsing systems, the majority of which are found to rotate non-synchronously with their orbits. Conclusions. The K2 mission is a rich source of data that can be used to find long period eclipsing binary stars. These data combined with follow-up observations can be used to precisely measure the masses and radii of stars for which such fundamental data are currently lacking, e.g., sub-giant stars and slowly-rotating low-mass stars.