The other answers are also correct, but a significant player in the tentacle's popularity was the anime *Urotsukidoji - Legend of the Overfiend* **1987** which was one of the first hentai to feature tentacles.

The reason it was so influential is that its sales were very good. Especially in the West, where it got a lot of media attention for its gore and rape scenes. Of course, this only drove more sales for the show. In Britain, it sold 40,000 copies at a time when the average convention was about 500 in attendance. For comparison, the only animated feature that sold more than this (by 1998 at least) was Akira.

(Ref: *Schoolgirl Milky Crisis: Adventures in the Anime and Manga Trad*e )

It was this show that started the term 'tentacle rape' and is also the source of early bad reputation for anime in Britain, and elsewhere.

As hentai shows were quite new then (The first hentai anime débuted in 1984), the commercial success of the overfiend probably contributed heavily to it's future repeated use in erotic animation.

**Other Reference:** 

*The Animated Movie Guide By Jerry Beck*