We report three newly discovered exoplanets from the SuperWASP survey. WASP-127b is a heavily inflated super-Neptune of mass 0.18±0.02 MJ and radius 1.37±0.04 RJ. This is one of the least massive planets discovered by the WASP project. It orbits a bright host star (Vmag = 10.16) of spectral type G5 with a period of 4.17 days. WASP-127b is a low-density planet that has an extended atmosphere with a scale height of 2500 ± 400 km, making it an ideal candidate for transmission spectroscopy. WASP-136b and WASP-138b are both hot Jupiters with mass and radii of 1.51 ± 0.08 MJ and 1.38 ± 0.16 RJ, and 1.22 ± 0.08 MJ and 1.09 ± 0.05 RJ, respectively. WASP-136b is in a 5.22-day orbit around an F9 subgiant star with a mass of 1.41 ± 0.07 M⊙ and a radius of 2.21 ± 0.22 R⊙. The discovery of WASP-136b could help constrain the characteristics of the giant planet population around evolved stars. WASP-138b orbits an F7 star with a period of 3.63 days. Its radius agrees with theoretical values from standard models, suggesting the presence of a heavy element core with a mass of 10 M⊕. The discovery of these new planets helps in exploring the diverse compositional range of short-period planets, and will aid our understanding of the physical characteristics of both gas giants and low-density planets. Radial velocity and photometry tables are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (http://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/599/A3