I'm going on myanimelist to refresh my memory xD
In no order...
Fullmetal Alchemist (03 and Brotherhood)- An amazing anime is all I can say, both versions.
Neon Genesis Evangelion (NGE and Rebuild)- One of my personal favorites, if you enjoy robots and aliens
Fairy Tail- I usually don't like long anime but this is one of my favorites
Digimon- I love the series, Mostly the first and third seasons
Pokemon- I was a fan of the original series and most of Advance, kinda stopped after that
Ouran High School Host Club- It's hilarious and I love it so much
Higurashi/Umineko- The Umineko anime isn't that good but I enjoy the characters. The first two seasons of Higurashi are good...but don't watch these if you really hate blood/torture
Toradora- One of the cutest romcom animes I have ever seen
Soul Eater- so good
Azumanga Daioh- cute comedy about a 10 year old in high school
Pani Poni Dash- Basically Azumanga except the 10 year old is the teacher
Panty and Stocking- Hilarious...but I wouldn't recommend for young ones
Madoka Magica- If you like magical girls and crying your eyes out
Inuyasha- I basically grow up on inuyasha
I'm guessing by Disney you mean the Ghibli films? I love Disney and Ghibli :D
Paranoia Agent- Another one I wouldn't recommend for younger ones and if you get triggered by things like someone rollerblading around and bashing people with a baseball bat
Ghost Stories- oh my god...You have to watch the dub...and be older and have a dark sense of humor
Elfen Lied- Don't like blood, nudity...don't watch. And if you don't feel like bawling your eyes out
Ga-rei Zero- More tame than Elfen Lied...but still the same things apply...but one of my favorites
Death Note- I don't have much to say since most have seen it...it's great tho
Buso Renkin- A nice shonen anime
Sailor moon- my childhood
B Gata H Kei- BE OLD ENOUGH TO WATCH IT...basically a girl's high school goal is to have her way with 100 guys, it's hilarious
Black Rock Shooter- Watch the OVA first, the actual anime that came out after wasn't as good
Nichijou- Super hilarious
Anohana- Tears will be shed
Worthy mentions.... that aren't anime but based on anime
Avatar the last airbender/ Legend of Korra- amazing series...i love them
Teen Titans- The best show in 2003
Anime Movies!!
Ghibli films....I'm not gonna list them lol
The Girl who Leapt Through Time- gee i wonder what its about...it's great tho omfg
Summer Wars- Did you like the Digimon movie that took place on the internet? Than make sure to watch this!
Wolf Children Ame and Yuki- One of my favorite movies, real tear were shed over it
Barefoot Gen- A tearjerker about life during the Atomic bombing in Hiroshima
Grave of the Fireflies- Ghibli but a lot of people overlook it, takes place during WWII and you will cry
Hotarubi no Mori E- I love this film, it's cute and heartwarming and then rips out your heart and eats it
You Are Umasou- This is a movie about dinosaurs, it's super cute about a carnivore adopting an herbivore
That's all for now! :D