Recent studies have recognised what could be the most massive volcano in the world, a geological feature already known, but was not recognised until recently as being a single volcano.
It is the Tamu Massif in the north-west Pacific (location map shown below), what was thought to be one of the vents of the Shatsky Rise - but recent seismic studies, reported in the article An immense shield volcano within the Shatsky Rise oceanic plateau, northwest Pacific Ocean (Sager et al. 2013) have revealed that it is one single shield volcano. The Geology.com article states that it covers an area of approximately 310,800 square kilometers (120,000 square miles), about "the size of New Mexico" - and, according to Sager et al., making it comparable with the size of Olympus Mons.
Location of the Tamu Massif
Map source: Daily Mail
According to the article Underwater volcano is Earth's biggest (Witze, 2013), that although the 140 million year old Tamu Massif is not as tall as Olympus Mons (nor even Mauna Kea) - in fact, it is still an impressive 4km above the sea floor, its 'footprint rivals that of Olmpus Mons', a comparison is shown below (the source is the linked article):
The authors hint that seismic studies could well find more shield volcanoes on a par or even more massive than Olympus Mons. Of course, as they state, the identification of Tamu Massif as a Olympus Mons sized megavolcano suggests that there have been more such megavolcanoes in Earth's early history, most of course would be eroded, lost to tectonic processes etc.