A number of datasets containing microlensing events have been made publicly accessible, including the following, summarized in Poleski and Yee (2018)

The NASA Exoplanet Archive actively encourages authors to share lightcurve data for published microlensing events: NASA Exoplanet Archive

KMTNet Survey Data

Photometry of microlensing events from 2015 (commissioning season, Kim et al. 2017) and 2016 data (K2/Campaign 9 footprint, Kim et al. 2018). These include 841 events and a further 266 candidate events. Additional datasets are likely to be made public also.
Kim et al (2017) Kim et al (2018)

UKIRT

UKIRT surveyed 18×106 stars in the Galactic Bulge (including microlensing events) in 2015 and 2016, and aperture photometry light curves have been released for the entire catalog Shvartzvald et al.(2018)

UKIRT Data Release

VVV

The VISTA Variables in the Via Lactea Survey in near infra-red passbands publicly released (Minniti et al. 2010) aperture photometry lightcurve data for all sources between 2010 and 2015.
Minniti et al.(2010)

VVV Data Release

Space-based Imaging Data

Time-series imaging data from the Spitzer Microlensing Program (2014--) and from K2/Campaign 9 (Henderson et al. 2016) are available from the NASA archives below.
K2 data in MAST

Spitzer data archive

OGLE

OGLE-II catalog of 2 × 105 variable sources in the Galactic Plane were published by Wozniak et al.(2002) and can be explored through the online archive:
OGLE Data Archive

214 OGLE-II/III lightcurves were published in Udalski et al.(2000)

3718 OGLE-III lightcurves were published by Wyrzykowski et al.(2015)

MOA

The lightcurves of 474 microlensing events were published by Sumi et al.(2013)

MACHO

The lightcurves of 564 microlensing events from the MACHO Bulge survey were published in Thomas et al.(2005)

2018 Roman Microlensing Data Challenge

The set of simulated Roman lightcurves produced by Matthew Penny for the 2018 data challenge dataset can be download from here.

Photometric LSST Astronomical Time-Series Classification Challenge (PLAsTiCC)

An extensive set of simulated lightcurves with a cadence matching that of the Rubin Observatory's Legacy Survey of Space and Time were produced for the PLAsTiCC PLAsTiCC data challenge and are available for download.

References:

Kim et al. (2017), AJ, 155, 76
Shvartzvald et al. (2017), AJ, 153, 61
Minniti et al. (2010), NewA, 15, 433
Henderson et al. (2016), PASP, 128, 124401
Wozniak et al (2002), AcA, 52, 129
Udalski et al (2000), AcA, 50, 1
Wyrzykowski et al (2015), ApJS, 216, 2
Sumi et al (2013), ApJ, 778, 150
Thomas et al (2005), ApJ, 631, 906