A long-term spectroscopic and photometric survey of the most luminous and massive stars in the vicinity of the supermassive black hole Sgr A* revealed two new binaries: a long-period Ofpe/WN9 binary, IRS 16NE, with a modest eccentricity of 0.3 and a period of 224 days, and an eclipsing Wolf-Rayet binary with a period of 2.3 days. Together with the already identified binary IRS 16SW, there are now three confirmed OB/WR binaries in the inner 0.2 pc of the Galactic center. Using radial velocity change upper limits, we were able to constrain the spectroscopic binary fraction in the Galactic center to F-SB = 0.30(-0.21)(+0.34) at a confidence level of 95%, a massive binary fraction close to that observed in dense clusters. The fraction of eclipsing binaries with photometric amplitudes Delta m > 0.4 is F-EB(GC) = 3% +/- 2%, which is consistent with local OB star clusters (F-EB = 1%). Overall, the Galactic center binary fraction seems to be similar to the binary fraction in comparable young clusters.