When it comes to Anime I'm fairly new to the scene, but I've watched my fair share of Anime and here's some of my all time Favorites. Pick one and I promise you will not be disappointed.
I like Anime that is not your stereotypical fighting anime such as Dragon ball Z. Now don't get me wrong, I love DBZ but I'll much rather watch an Anime that has a complex and intriguing Story-line. Preferably a complex time travel story-line.
(Anime is not in any particular order, these are simply my favorites)
A time travel adventure that has paradoxes and many of the complexities that comes with a time travel story. If you google the "best Time travel Anime of all time", this anime will pop up and for good reason. It does everything right with no filler just pure great story-telling.
If you do decide to watch this Anime be sure and re-watch the first episode again after you finish the series.
Time Travel greatness.
Erased is a fairly new Anime which began early 2016 and since then it has been praised as the best Anime for 2016 despite the year being only a few months in.
This Anime deals with time travel and a mysterious murderer. It deals with the paradoxes that comes with trying to change the past. (a butterfly effect)
The cinematography is absolutely beautiful. No other Anime has this level of sophistication when it comes to "camera work". Definitely one of the best Anime I've ever seen. (By the way, the series hasn't ended)
This Anime is pure "Smarts", it was created by a group of pure geniuses. Seriously, this Anime is very hard to predict because of the crazy plots and crazy twists. When I discovered this anime, I ended up watching the entire series in two days and it had me wishing it was much longer.
It involves two smart men trying to out dual each other and only one has the power to kill the other but only if he could learn his real name.
The deathnote grants anyone the ability to kill anyone only if they know their real name and have seen their face somewhere.
The premise is absolutely brilliant.