I don't know what genres you like/watch but I highly recommend Space Brothers. It is amazing. It is long and slow but it is just so good.
It depends on the type(s) you're looking for, I'll list a few along with it's genre; Steins;Gate (Sci-Fi/Thriller) Mirai Nikki (Action/Thriller) Elfen Lied (Action/Psychological) Death Note (Mystery) Shiki (Horror/Mystery) Angel Beats! (Supernatural/Comedy)
Hunter x Hunter Hell Girl Rozen Maiden Another If Her Flag Breaks Watamote One Punch Man Sankarea FLCL Denpa Onna to Seishun Otoko Kill La Kill Madoka Magica Panty and Stocking with Garterbelt Mirai Nikki I could list a whole lot more, but I'm just kinda throwing stuff out there with no direction. Also I wanna throw out Sky Girls because I need more people to talk to about it there's like nobody in the fandom please help
Deathnote Fullmetal Alchemist Brotherhood - less filler than the other version Trigun Ghost in the Shell - all of them Apple Seed Hellsing Ultimate - less filler and closer to the manga Less serious but I enjoyed them both are Girls Un Panzer - its funny and I like tanks RWBY - not finished but good mix of humor and ass kicking
"I'll take this potato chip... AND EAT IT!" I don't watch anime any more but I used to really like Hetalia and Attack On Titan - which are complete opposites, I know. Ooh, also Ouran High School Host Club. I can feel myself being judged.
Ah yes Hetalia is one I can really recommend or if you like yaoi/Boys love then you should totally check out Junjou Romantica or Hybrid child. These are awesome too: Free! Enteral summer Owari no seraph Orenchi no fuo jiou Magi Labyrinth of Magic
I would also suggest Re: zero but it's also still airing so it's not complete yet. I haven't seen the anime but I have played the Steins;gate game which is one of my favorite games. I've heard the anime did a really good job adapting it so you should at least check it out.
Attack on Titan if you're into some gory/sad stuff with a lot of action. Tokyo Ghoul, gory/sad too, with a lot of action xd Ajin, supernatural as hell and it's 3d-ish. Erased, a mystery anime. Doukyuusei, it's an anime movie but it's probably the best movie BL ( boy's love ) out there. Free! and Haikyuu for sport animes ( btw the ships ( romantic pairing that is/(but mostly) isn't real ) are crazy on these kinds of anime ) Beyond the Boundary if you like a cute girl with an epic sword and romance. Sakura Trick for some cute and funny lesbian romance. Sao ( Sword Art Online ) cause it's just plain amazing. Zankyou No Terror, a lot of explosions. Have fun! ^^
Code Geass Elfen Lied Parasyte Berserk (1997 original series + 2016 series continuation) Deadman Wonderland Blood + Gantz (Warning: Very Graphic) Mushishi Black Butler Tokyo Ghoul Neon Genesis Evangelion
My recommendations: Tokyo Ghoul Attack on Titan Hunter X Hunter Soul Eater Death Note Gate God Eater Elfen Lied Fate (Stay night and Zero) These are the ones that immediately come to mind, but there are more. Just depends on your style, most of these revolve around action. If drama is more your style, then I have a bunch more that I could list
Tokyo ghoul and associated Gintama and associated Arslan senki and associated (ahhhh new season!) Berserk and associated (abhhh new season yay!!) R rated Deathnote Mariaholic Everything by studio ghibli, nausicaa and ocean waves are my favorites Boku no pico, it is a rite of passage DurarRararaarararararararararararararararar and associated Some of my favorites and one pile of garbage
Can't believe no one has mentioned Cowboy Beebop Yes Naruto is awesome, love both part 1 and Shippuden my all time favorite anime, its even in my top 10 fav shows of all time (we'll both part 1 & Shippuden are included)