Roberto Martinez said that Villarreal got the Yellow Submarine nickname because of their back-and-forth between La Liga and the Segunda in the late-90s/early 2000s:

"Villarreal picked up the nickname El Submarino Amarillo or 'Yellow Submarine' from the period when they were yo-yoing between La Liga and the secunda division, they were getting relegated, coming back up

"Now they are more a stratospheric type of team and they don't deserve that nickname anymore"

I had never heard this as the background - anyone else have any input on that?  I always just figured it was because the yellow unis are fairly unique. 
If you want more background on the history of Villarreal's choice of yellow uniforms (which one way or the other factors in to the nickname), check out this post from the old site (which will soon be available at Villarrealusa.com, as our archives are transferred over!):

Villarreal, from near Castellón on Spain’s eastern coast, made their debut in the top flight in 1998 and brought an unusual kit story with them. Nicknamed, rather obscurely, the Submarines (allegedly after the Beatles song) their yellow shirts date back to 1947 when the son of the club’s president travelled to the nearest big shopping city (Valencia) to buy some replacement white shirts and black shorts – then the team’s official colours. Unfortunately, when he got to the store there were no white shirts in stock and, with the season about to start, he panicked and bought the only batch remaining, which happened to be yellow. On returning to Villarreal the players thought the shirts were fine, but that they didn’t go too well with the black shorts. The president’s son, decisive if nothing else, travelled to Castellón this time and bought a batch of white shorts which he subsequently had dyed blue on the vote of the players. The club still sports the combination initiated by this act of democratic aesthetics. 

--From Phil Ball's book, Morbo, The Story of Spanish Football.