There is a lot of anime series that are considered to be popular. There are some people who will say that they only watch Death Note. Others who would love Pokemon shows with more of a PG rating may like Pokemon more. There are other anime series that have gotten popular over the past years. You can mention Dragon Ball to any anime fan and it is likely that this person has watched at least one episode.
Other most-watched anime series are Naruto, Bleach, and Fullmetal Alchemist just to name a few. There are also some anime series who have gotten popular recently and these anime series are being watched more now as compared to the others.
Due to lack of ability to accurately calculate the precise number of episodes and animes watched, this may not be a completely accurate list, but we can get pretty close. After checking a few commonly used, popular anime websites that due track the number of people watching the anime with the most people who have watched it is Fullmetal Alchemist. Brotherhood.
A close second after Fullmetal Alchemist Brotherhood is Death Note. Taking 3rd place is Bleach, which is a very popular anime similar to Naruto. Each of these anime have been watched millions of times.