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For #1: Apparently there was a 1998 TV series called "Back To Sherwood" that sounds similar: "Robyn Hood, (not the one from the book but a modern day teenager) travels back in time to discover that she is in Sherwood Forest where the famous Robin Hood once lived. Using a magic amulet, given by her grandfather she has to rescue her famous ancestors from a wicked sorceress."
Number 1 sounds like a Canadian children's series called "Blizzard Island", which featured a brother and sister with a transporting amulet, as well as a character called Argon. Apparently the series spawned a direct-to-video movie called "The Argon Quest", which may have been what you saw.
Edited by GordonWayEmbryon - It wasn't Secret of Nimh. The sick mouse wasn't the premise, it was only a plot point. I looked into it (and Once Upon a Forest) months ago knowing it would be the first thing everyone suggested.
- 3 wasn't the pebble and the penguin, either. Like I said, way, way obscure.
Gordon - Oh my God! That was it. The Blizzard/dying island thing brought it all back to me.
Thanks for the suggestions Fifi - I see you in here trying to help everyone.
http://www.amazon.com/Adventures-Scamper-Penguin-Virginia-Masters/dp/B000CCD20G/ref=pd_cp_mov_1
One more tip until dinner. Amazon suggested this with the "Willy the Sparrow" search.
The last one isn't one of the American Tail movies, is it?
Edited by smashingmelons Otherwise known as [Smashing Melons 42].I really thought it was an american tail movie. I've been brainstorming with my brother all night, he says he remembers something about the daddy mouse being away at war, which made me think of AAT. I think it was something of a country mouse/city mouse theme, which kind of fits in with AAT as well. The only snag is, I'm almost positive it wasn't musical.
FIFI - can you give me a link to "A Real Mother?"
Edited by Tsarevna"A real mother" is slang, shortened from "A real mother f*er" meaning something really difficult or bothersome.
As for the last one.. the only things I can come up with are Wind in the Willows, which I know isn't right, and maybe Redwall, since I've never seen the series (nor read the books) I don't know if there are humans in them at all.
Number 1 is called "Blizzard Island"
link: https://www.youtube.com/watch?v=VPUlOru5IIY&feature=related
The giant's name is Argone
Apparently it's called "Field Mouse Country Mouse" and it's a loose adaption of both the Robert Burns poem "To a Mouse" and the Beatrix Potter book "City Mouse Country Mouse". I can't find anything about it on the internet though. Cross your fingers that I can find the old VHS tape and look for a production company.

When I was a wee bairn (early-mid 90's) my mom had us subscribed to this monthly movie club (mom claims it was Focus on the Family's movie club). They were all pretty obscure I think.
1. This one was live action and I remember the name of it was The Argonne Forest, but google brings nothing up. It was about a brother and sister who find an amulet in their grandparent's house and it transports them to the Argonne forest. There's some kind of friendly rock formation who tells them they have to return the amulet to a rock in the forest to get home. The last scene has a bunch of kids returning other amulets - I think they were all trapped there until the main characters return theirs as well.
2. This one was an animated movie about a boy who was home sick and refused to do the homework his classmate brought after school. For some reason was turned into a blue bird. There's one really well animated sequence where he's flying around the town, and it's all brownstones and postcard churches. He then teaches another bird to read and write. May have had an "it was all a dream" ending
3. This one was also animated. It was about some penguins in Antarctica who were nabbed by men on a steamship. Most of them were family, but one was an emperor penguin named Sam or something. They all outwit the sailors and find their way home.
4. Last one, also animated. It was about some mice who live in a brick in a farmer's field. The farmer has begun plowing his field and planting crops, but one of the baby mice is sick and the mother doesn't want to move her. This is just the opening, I can't remember much more, except the sick mouse's little brother goes on some kind of adventure to find them a summer home. It wasn't Secret of Nimh or Once Upon a Forest.