Stitched applications
In old cartoons there is often _____ hanging on the wall, reading "home, sweet home" and the like, often framed. As far as this question is concerned, this stuff is sewen, stiched, knitted, you tell me. What is this thing called?
I'd call this Stickerei in German and the dictionary offers "(archaic) stitchery", but this applies broadly to any stitched decoration, e.g. on cushions, jackets. It also offers embroydery, fancy-work for synonyms. Tapestry seems to come close, but rather describes a hanging rug (a flying carpet, isn't it). Is any of these preferentially used to describe the stitched plaques, is plaque a good fit, or are there specialized dialectal terms? And what's up with that anyway, what's the tradition called?
Reason I'm asking is this Ger "Applikation" describes embroydery, funny enough, and through the correspondance p ~ f may relate to Flicken "plug, patch". patch-work has gained a different sense, though. Ger Stepp- could relate to tape-, but I am not sure.
Solution 1:
Sampler or cross-stitch sampler
(Cross stitch is a particular type of embroidery.)
Here is a short article that gives you some terminology and will also help you understand how embroidery fit into women's life course in the 18th century: American Needlework in the Eighteenth Century
A how-to book with images and some historical information, Cross Stitch Antique Samplers, states:
The term 'sampler' comes from the Latin exemplum, meaning an example to be followed, a pattern or model.
(Wall hangings would most often hang from a dowel rod. Which is not what you saw in the animated films.)
Here is an example of a "Home Sweet Home" sampler from an old animated film, which I found with a Google Images search.
Now, your sample sentence:
In old cartoons there is often a sampler hanging on the wall, reading "home, sweet home" and the like, often framed.
Solution 2:
It would actually be a proverbial embroidery, however it would be referred to as an embroidery in UK English. But according to my dictionary that is not how the word embroidery is used in US English. Although as I have already stated it is a proverbial embroidery I fined no actual use of this term on the Internet. But there are many for embroidery and wall hanging.
Embroidery Kit Link
A more general term for things similar but not exclusive to an embroidery sign is Wall Hanging
wall hanging noun; a large piece of material or sewing that is hung on a wall as a decoration
embroidery noun UK (SEWING) patterns or pictures that consist of stitches sewn directly onto cloth:
proverbial adjective (of a statement) commonly known, esp. because it is from a proverb or saying known by many people, or because it expresses a truth known by a particular group of people:
All references Cambridge English Dictionary