well, idk what my fav anime is, but i can mention some that has inspired me with many things,
sword art online: made me strive to make great games one day.
neon genesis evangelion: helped me understand myself a bit better.
death parade: made me value all my days alive.
Then there are some other animes that idk waht to say about
I owe a great debt to the DiC dub of Sailor Moon (without which I would never have gotten into geekdom). But my favourite anime has got to be Galaxy Express 999. I love trains, and the plot of each episode leaves you thinking about the fundamentals.
Honourable mention also goes to Ah! My Goddess! Keiichi and Belldandy are adorable! :3
All by Studio Ghibli (though miyazaki preferred they be called animation because he dislikes "anime" lol)
Ghost in the Shell, definitely.
TRIGUN, without a doubt.
Code Geass for sure!
Death Note because of course.
The Melancholy of Haruhi Suzumiya, because hell yes.
Attack on Titan
Higurashi no naku koro ni
Bleach (the first 3 arcs)
And too many others. Been a fan so long it's getting hard to find anime that I haven't seen that isn't littered with fanservice...