I find Anime is usually dismissed for a few reasons. The first is that like foreign films, people fall under the assumption that it requires an acquired taste, for those who enjoy subtitles (please love yourself and don't watch badly dubbed anime!!!) and for those who care about Japanese culture. The second is the medium itself - everyone knows cartoons are for children. The third is that the terrifying fanbases can put people off, which links to both the first and second reasons - Anime is only for people who are crazily obsessed and who often cross the border.
Whilst I'll admit I have grown up with it on TV as the alternative to Disney Channels and so on, and therefore probably have a better cultural knowledge of it that makes it more accessible to me, I'll make a case for it actually being really accessible to anyone. A lot of the humour and stylisation of anime (despite the huge range of subgenres, there are definitely conventions to the medium itself,) might seen very - wait for it - foreign to nonviewers, but it's (a) not particularly... difficult to follow or make sense of, and (b) you really do become more accustomed to it the more you watch.
I'll also suggest that these conventions are what make anime series really good. Series can last anywhere ranging from 6 - 400+ episodes so it really depends what you're after, but because most of them are based on long-running manga series, there is plenty of character and plot development that can take place. Flashbacks and revelations through flashbacks are a really popular device, and the best series utilise plots within plots to give you a really in depth understanding of the characters and the world they inhabit. To touch upon the fictional worlds as well, anime diegeses are usually incredibly complex. Due to the long runtime of series and detail the manga is able to go into, the fictional world and its coherent rules and established and understandable, often expanding as we learn more about plot x and y. A lot of it does require commitment to a series, its characters, and its rules, but that's the joy of 20 minute episodes that there are a LOT of. Easy and fun to consume!
Attack on Titan, found on google.
Although it's a cartoon and therefore for CHILDREN, anime is actually not for children. Well, some of it is, but a large majority of popular ones that people on the internet rave about (because that's the judging factor we are using here apparently,) are for a teenaged + audience. Plots are thus gory as heck (Attack on Titan being one of the goriest I've seen...) and complicated enough for an intellectual audience (again, depends on the actual genre / anime you choose.) It's pretty easy to get sucked into a series with good characters, promising plot, and a believably set-up yet mysterious fictional diegesis, right?
Ouran High School Host Club, found on Google.
As said, however, all of this depends on the genre of your choosing. If you prefer romantic-dramas, you'll probably prefer a shoujo anime like the hilarious Ouran High School Host Club (my favourite!) or Toradora, and if you like Sci-Fi you might like mecha like Gurren Lagann or Code Geass. Horror fans might like series such as Elfen Lied, and if you like straight up action, there are ninjas (Naruto,) death gods (Bleach,) and brothers on an epic quest to bring their mother back to life (ish) (Full Metal Alchemist - watch Brotherhood over the normal though.)There is of course, a huge extensive collection of all subgenres within anime so these are just a few off the top of my head, and some of the most well known ones as well.
Of course, I'm recommending Attack on Titan to anyone for messing me up like few others have done before. Rarely are TV series so expendable on their characters (yes, I do watch Game of Thrones as well,) and the battles are wonderfully gritty and exciting. Predictability is a feature you do need to be wary of due to Anime (or more realistically, the manga they are based off)'s conventions. New series keep things fresh however, and Titan is a huge contender for one of the best things I've seen pretty much ever.
In short, give something a chance if you're bored. There's a series for everyone, and most of them incorporate all elements into their stories; I've laughed in horror/gory/intense action animes just due to the ridiculous humour and convention and have been left weeping over endings (Chrono Crusade, I'm looking at you.) Either way, it's easy to watch, easy to find, and offers something a little bit different. OH, but it's really addictive. I guess that's why there are so many rabid fans.
