Don't seem to see one of these so gonna get a ball rolling here for future furniture suggestions so that artists may perhaps get ideas/design based on popularity etc. (Not really sure what to put for a tag, so hope I got it right)

Anywhere:
-New Food Types - Parfaits/Sundaes/Icecreams/International Desserts, Appetizers & Snacks, Main Course Meals
-Balls - beach balls, soccer balls, volley balls, watermelons, balloons, tennis balls etc (pets need some toys!)
-Carpets/Rugs/Picnic Mats/Towels
-Flower Vases for tables


Inside House:
-Kitchen Utensils to hang on walls (tiny frying pans, spatulas etc); Kitchen Stove/Fridge/Shelves/Oven/Mircowave etc for the ground etc. (We already have the kitchen floor tiles to match afterall)
-Partitions/Partition Walls (so that players may create illusions of rooms within a room), or like Japanese folding partitions
-Standing Lamps/Candles/Wall Lamps
-Pillows/Cushions/Beanbags to put on the new couches (stacking?) or just plain put on the floor.
-Beds - Single, Double, Queen, King, Princess, Futons, Sleeping Bags
-Wall shelves
-Long tables & matching chairs
-Toys : Easels, Game console, Rubber Duckies, Chess board, Building blocks etc. TV/Wall Mounted TV
-Display Shelves (where players could display certain items perhaps?)
-Bathtub


Backyard/Frontyard:
-Mail Box
-New Plant Types - ie Daisies, Sunflowers, Roses, Orchids, Lilies, Veggies(Wheat, Rice/Padi, Carrots, Turnips, Cabbages, Corn etc (for dem farmers)) to name a few.
-Trees - ie Fruit Trees, Stumps, Dead Trees, Sakura blossom trees, logs etc.
-Fountains, Bird baths
-Ponds (perhaps players could hoard for different fish to put into ponds so kind of like a stackable furniture)
-Beach themed stuff - Picnic Tables; umbrellas (would be perfect to place sodas and icecream outdoors *cough*)
-BBQ Grill/Pit
-Swing
-Pruned Bushes/Hedges in pixpet shapes
-Tents & Camping stuff (campfire, outdoors sleeping bags, fishing poles etc)
-Rotatable Hedges/Fences allowing players to make their own hedge mazes :x

With regard to Partitioning: Things like Fences would look odd in the middle of an isometric square so suggestion to have the image created to line the edge of a square that can be rotated and thus joined easily while creating the illusion of space. If the Partition is thin enough then it can work similar to the tables and couches and allow a pixpet/some other item to share the same tile without creating a weird gap far away from the fence if it were cutting through the middle of a square.

Just off the top of muh head, will prolly edit when think of other things
Cheers~!