Let’s list some lesser known but still awesome movies.
The Brave Little Toaster
Many Don Bluth films.
The Snowman (watch it here) SERIOUSLY WATCH IT!
Melody Time
The Adventures of Icabod and Mr. Toad
Nausicca and other Miyazaki films
The Phantom Tollbooth
Rikitikitavi
THE SNOWMAN!!! ^_____^ I watched that ALL THE TIME when I was kid and I found it on YouTube last year and I honestly got choked up. I don’t get cinemotional AT ALL pretty much. ^^
Iron Will
Zeus & Roxanne
Popeye (the Robin Williams movie)
The Adventures of Rocky & Bullwinkle (the movie - yeah, call me a geek 
)
Cats Don’t Dance
Scamper the Penguin 
I think I saw that as a kid, but got it mixed up with a cartoon version of Wind in the Willows I used to always watch but can’t find on the internet nor in my house.
Some more underrated films:
Swan Princess
Thumbelina
The Pagemaster
… I can think of more but only Don Bluth ones. I’ll name those-
All Dogs Go To Heaven
An American Tail
Rock-A-Doodle
The Secret of NIMH
CGI Clownfish: I love Cats Don’t Dance! The singing is somewhat annoying to me and embarassing, but otherwise it was an awesome film! I just rewatched it recently.
I love all of those that you listed, FONY, apart from Thumbelina which I never had the chance to see.
I wouldn’t say The Snowman is not well-known…It’s like a thing that everyone on the entire planet has to watch it at least once at Christmas. 
I can’t think of anything else at the moment. I adore A Scanner Darkly, which is pretty unknown, but although it’s animated it’s not exactly for kids or anything.
lizardgirl: Since you haven’t seen Thumbelina, I suggest you don’t unless you’re able to stomach the cornyness. ^^; I loved it a lot when I was little, but upon watching it again all I could think was … “What the heck was I on?” It’s pretty good, but very happy.
I hate myself for not mentioning Fern Gully - one of the best non-Disney films out there IMO.
The Adventures of Milo and Otis
I looove this film so much! It’s my favorite live action film about animals and my second favorite dog movie (next to Fox and the Hound).
When I see more lesser known movies that turn out to be among my favorites, I’ll post 'em here.
Pshaw. Lesser known in the US maybe… Porco Rosso is my fave of Ghibli films at the moment.
Hmm… how about Spirit (the horsey one… can’t remember the subtitle) and All Dogs go to Heaven!
(scrolls up a bit)
Dang, I got beat to that…
Also, total agreeance with you on Phantom Tollbooth, Glyph. It brings back very vivid memories because it was the first movie that I was angry at for being completely different from the book. They left out like half of the characters! How dare they!
YES. I grew up on that. Just watched it for the first time in years yesterday, actually.
This was a tough topic for me to get myself involved in, since most of the animated movies I have watched so far are either Disney or Pixar productions. However, I thought of one just seconds ago; “The Polar Express.”
It is heartwarming, it possesses a Christmas theme (I love Christmas themes), and it has Tom Hanks’ voice in it.
I’m not a very good judge of how well known a movie is but here we go anyways:
Don Bluth
All Dogs go to Heaven
An American Tail
Rock-A-Doodle
The Secret of Nimh
The Pebble and the Penguin
A Troll in Central Park
The Land Before Time (loved this as a kid)
The Funtastic World of Hanna-Barbera (a ride film with beautifully animated classic characters)
Thumbelina (never seen it)
Fox Animation
FernGully: The Last Rainforest
Once Upon a Forest
The Pagemaster
Anastasia
Titan A.E.
Universal/Amblimation
Balto
An American Tail: Fievel Goes West
We’re Back! A Dinosaur’s Story
A Wish for Wings That Work
WB Animation/Turner Animation
Cats Don’t Dance
The Iron Giant
Eight Crazy Nights
Dreamworks
The Prince of Egypt
The Road to El Dorado
Spirit: Stallion of the Cimarron
Sinbad: Legend of the Seven Seas
Walt Disney Feature Animation
Melody Time
Three Caballeros
The Adventures of Icabod and Mr. Toad
Song of the South (while not totally animated, what is there is some of the best animation ever done)
Disney Toon Studios
The Brave Little Toaster
Pooh’s Grand Adventure
The Tigger Movie
Studio Ghibli
Nausicaä of the Valley of the Wind
Laputa: Castle in the Sky
Grave of the Fireflies
Pom Poko
My Neighbor Totoro
Kiki’s Delivery Service
Porco Rosso
Whisper of the Heart
Princess Mononoke
Spirited Away
The Cat Returns
Howl’s Moving Castle
Little Nemo: Adventures in Slumberland (would’ve liked to seen Miyazaki’s version)
Production IG
Ghost in the Shell
FLCL
and lastly
The Chipmunk Adventure (it’s a miracle that this movie was ever made)
Hopefully some of these were off your radar and I encourage you to check them out!
Ooh, I’ve got one! Flushed Away.
Okay, not unknown per se, but under appreciated for sure. Go Arrdman!
There’s CBSFox/ IFC’s The Last Unicorn (1982) - one of my favs,an it is very Special to me, there’s A few others that our my favs like.
Princess and The Goblin (1994)
The Secret Garden (1994)
Warner Independant/The Snow Queen (1994)
Tooniversal’s Marco Polo (2003)
Hallmark’s Dinotopia - The Animated Movie (2005)
Toy Warrior (A TV Movie in 2005)
Teletoons Silverwing - A Glimpse Of The Sun,Towers Of Fire,Redemption Tv Movies (2005)
Cricket In Times Square A Short Film (1977) ect.
Invasion America - Final Mission Tv Movie (1998)
Ambline’s Pinky And The Brain - Brain Drained Tv Movie (1998)
Disney’s Mighty Ducks - The Animated Movie Tv Movie (1996)
Disney’s DarkWing Duck The Movie - Darkly Dawns The Duck (1991),Just Us Justice Ducks Tv Movies (1992)
Disney’s Chip N Dale Rescue Rangers To The Rescue Tv Movie (1989),They Shoot Dogs Dont They 2 Parter -Tv Movie (1990)
Disney’s Tale Spin The Movie - Plunder And Lightning Tv Movie (1990)
Ambline’sTiny Toons Adventures The Movie - How I Spent My Summer Vacation (1991)
Warner Bros. Superman - The Animated Movie (1996)
Warner Bros. Batman - The Animated Movie (1992)
Phil Romans Mighty Max The Movie - Pandor’s Box,Apocolipse (1993)
USA’s Highlander - The Animated Movie (1994)
Dic’s Double Dragon - The Animated Movie (1993)
ThunderCats - The Movie (1986)
Transformers - The Movie (1986)
Nelavana’s Carebears The Movie (1985),Carebears The Movie 2 (1987)
Dic’sSonic The Hedgehog - Blast To The Past - Tv Movie (1993)
Dic’sSonic Underground The Movie - Beginnings - (1999)
Sonic The Hedgehog (1999) (Anime)
My Little Pony - The Movie (1987)
Rainbow Brite - The Movie (1986)
Dic’s Kissy Fur - The Movie (1985)
Hanna Barbera’sThe Good,The Bad,and The Hunkle Berry Hound (1897)
Universal’s The Jestsons - The Movie (1990)
Warner Bros. Quest For Camlot (1998)
Hallmark’s The Ugly Duckling (1997)
Dic’s Heathcliff -The Movie (1988)
Warner Bros. The King And I (2000)
Xyber 9 - New Dawn - The Movie (1999)
Columbia’s Jackie Chan Adventures - The Movie (2000)
Nerdcorps Dragon Booster - The Movie
Canada’s Skyland The Movie - (2005)
Nerdcorps Storm Hawks -The Movie (2007)
Larry Shartz’s Speed Racer The Next Generation Animated Movie (2008)
Water Ship Down (1977)
Redwall (1985)
That’s all I can think of at this time,I know of an Watched,Love,or Know of,from me finding out,my Friends,Family,sorry if I might one repeated some ect.
Now I totally need to find my copy of this on VHS. I loved this movie when I was little!
Maybe I’m just going on a Pixar craze here, but when I saw The Snowman, the end reminded on Monsters, Inc, how the boy/Boo would go outside/open the closet and expect to find his/her new friend there, but Sully/the Snowman was gone. But both had been real. Sully was, for sure, and the Snowman was, because he still has the scarf on from when the boy went outside with him. But even though the door was shredded/the Snowman melted, a year later the door is put together again/it will snow again and the boy can make another snowman. 
And the Velvetten Rabbit reminds me of Toy Story 2, about being given up.
Anyway, a film I really enjoyed but isn’t that popular is The Adventures of Sharkboy and Lavagirl. Some people are really critical about this movie because they think it’s childish. But in my opinion, no matter how childish it seems, it has a deeper message in it, that dreams and imagination are important, but you need to work to make them come true, and still work to keep them. And I thought it was really nice that the story and characters are based on a little kid’s, and his father put them into a movie. I wish I could do that.
How about James and the Giant Peach! I haven’t seen that movie in forever…
I was always a sucker for cartoon + reality crossovers
You mean like Enchanted, Who Framed Roger Rabbit, and Alvin and the Chipmunks?
Pixelated- I love James and the Giant Peach! Centipede was always my favourite, and every time I see the film, I always enjoy pointing out the scene which features Jack Skellington from the Nightmare Before Christmas. It’s endlessly amusing.
David: Aww, I love that movie! x) That was always one of the movies we never saw enough as a kid, because we’d misplace it and whine about never seeing it enough. xD My favorite character was Mr. Earthworm. I felt so sorry for him on that bit when they tickled him to make him wiggle and get the seagulls’ attention. xD
what about a little British film that came out this year called…
SON OF RAMBOW
It’s great! Just see it! (no it’s not about Sylvester Stallone being tough)