Villarreal and Celta have met 18 times in the league (all in the Primera Division), with an overall record of 6 wins for Villarreal, 4 draws, and 8 wins for Celta. (In El Madrigal, we are 5-2-2).
However, all but four of those matches were played in the 1998-2007 period. Celta went down to the Segunda, and came up just in time to miss us going down.
In the recent history, Villarreal won both matches last year, 3-1 there and 4-1 in El Madrigal; the year before that, Celta defeated us 2-0 in El Madrigal (the infamous smoke-bomb game), and there was a 0-0 draw in Vigo that I honestly remember nothing about.
Largest Villarreal victory at home: 5-0 in May 2003. Celta had two men sent off in that one, and all the goals came in the second half. Celta's manager at the time was a certain Manuel Angel Lotina, so I'll simply say the trivote didn't work :)
Biggest Celta victory away: 0-2, February 2014.