There was a time when anime was truly very popular in Japan. There was a time called Anime boom wherein people were able to watch up to 2 series a week that they considered good and worth watching. The first anime boom started in the 1960s. This was because of Astro Boy. Other anime series followed suit. Another popular anime series at that time was Obake no Q-Taro.
This is a comedy-fantasy series that some people still rave about at present time. The anime boom ended when there were other series that were being shown on television. There were some mini-programs that were not related to anime anymore. Anime is still well-loved right now but the boom ended around the early 2000s. Who knows, a boom may start yet again.
The anime world has experienced 3 "booms" in the past and maybe feel that anime is in it's fourth boom. There seems to always be the same catalyst throughout all anime booms causing a rise in popularity. This is caused by a new anime being released which grabs the attention of the audience. From there it seems that societies love of anime is quickly rekindled as they search for new anime to watch and thus creates a boom.
The first boom happened in 1963 when the anime Astro Boy was released and became very popular. The next anime boom was in the late 70s to early 80s with the release of Urusei Yatsura, The Movie: Space Battleship Yamato, Mobile Suit Gundam, and Macross.