M87 is a nearby radio galaxy that is detected at energies ranging from radio to VHE gamma-rays. Its proximity and its jet, misaligned from our line-of-sight, enable detailed morphological studies and extensive modeling at radio, optical, and X-ray energies. Flaring activity was observed at all energies, and multi-wavelength correlations would help clarify the origin of the VHE emission. In this paper, we describe a detailed temporal and spectral analysis of the VERITAS VHE gamma-ray observations of M87 in 2008 and 2009. In the 2008 observing season, VERITAS detected an excess with a statistical significance of 7.2 sigma from M87 during a joint multi-wavelength monitoring campaign conducted by three major VHE experiments along with the Chandra X-ray Observatory. In February 2008, VERITAS observed a VHE flare from M87 occurring over a 4-day timespan. The peak nightly flux above 250GeV was 7.7% of the Crab Nebula flux. M87 was marginally detected before this 4-day flare period, and was not detected afterwards. Spectral analysis of the VERITAS observations showed no significant change in the photon index between the flare and pre-flare states. Shortly after the VHE flare seen by VERITAS, the Chandra X-ray Observatory detected the flux from the core of M87 at a historical maximum, while the flux from the nearby knot HST-1 remained quiescent. Acciari et al. (2009) presented the 2008 contemporaneous VHE gamma-ray, Chandra X-ray, and VLBA radio observations which suggest the core as the most likely source of VHE emission, in contrast to the 2005 VHE flare that was simultaneous with an X-ray flare in the HST-1 knot. In 2009, VERITAS continued its monitoring of M87 and marginally detected a 4.2 sigma excess corresponding to a flux of ~1% of the Crab Nebula. No VHE flaring activity was observed in 2009.