Well if we're being sincere, the Dragon ball franchise is the oldest and most popular anime but given the fact that alot of people might not know it's anime or consider it as such.
The next available option would be the Naruto franchise, ore specifically Naruto Shippuden. This anime is the most widely accepted anime in the world and to prove that, it's movie "The Last" that showed in cinema's made over a billion dollars, which is not an easy task for a movie much less an Anime.
Another anime I think might be a contender is "One Piece" although I'm not a fan of this anime I think it is quite popular and it's definitely the longest running anime available currently.
If it is based on my opinion alone, I will say Naruto. The anime basically ushered us into a new era of mainstream anime acceptance because of how good it is.
It became so popular that it ran for more than 20 years and still runs by virtue of a spinoff called Boruto, which remains largely popular and successful
In my opinion, One Piece is the most popular and most watched anime. A lot of people all over the world know and watch the series. Even in Japan, some people who don't usually watch anime, watch One Piece.
I can actually say the same for Dragon Ball and Naruto. However, these two anime are already completed. As for One Piece, it's ongoing and is aired every week. It's original manga is also read by many people all over the world.
One Piece isn't really my favorite anime, but I enjoy watching it every week. :)
Definitely Dragon Ball Z. There's no anime fan out there that hasn't heard or watched Dragon Ball Z. It's so popular it got its own movie adaptation.
Definitely Dragon Ball Z.
I've been a Dragon Ball Z fan since I was 9 years old. So over 20 years now. So I'd say DBZ for life! But that's my own preference. There's a lot of people who watch Naruto! And a lot of people who are into an array of other anime shows. But those are the two main ones.