I would say the evolving items..
Evolving Chicken Egg
Evolving Ant Farm
Evolving Toy (stage3)
Also Evolving Snow Globe and Aquarium..
That is was what they looked like when they started:
They turned into 4 different items each..
Below is the Evolving Piggy bank (stage 2) and the (Toy Stage 2) Toy Started as a Ball.
My raset item/items that I would find rare on the NA server would be...
All my Irem stuff.
The 2009 Female Vampire costume. (Although I never did get the bottoms.)
Gaggle of Goslings Companion (Although it may return.)
Nativity Scene, Kwanzaa Candles (Kinara), Menorah Furniture items
Resident Evil 4 items
Namco Museum furniture/clothing rewards from the spaces.
EA Sports clothing and item rewards
Xi Butterfly Ornament and *Ninja Figurine
Model of Rachet's Ship
Uncharted 2 Clothing and Furniture reward items
PlayStation Home Mod Furniture reward.
Original Playstation (PS One) Furniture reward.
Scion Furniture/Clothing rewards
2010's Halloween rewards
Ford reward items
Dead Island reward items
Central Plaza Sourvenir Item (I kind of wish this item could Teleport you to CP.)
PlayStation Vita rewards
Conspiracy reward/purchased items.
E3 2010 rewards
Gold/Animated Gold Picture Frame, Valentine's Day Picture Frame (Old Mall), Tauntaun Taxidermy.
Alien Invasion Lava Lamp Trophy (gold)
Ran out of room more to come
UFC Rewards/Personal Space
Redbull Personal Space/Rewards
Ninja and Pirate outfits (Costumes store.)
inFAMOUS Space rewards/purchased items
Street Fighter 4 Alt costumes
Open Beta Anniversary T
Legion T-Shirt (As it has my date of birth on it.)
PlayStation Move items
Venetian Carnival Mask (Not sure if it's still available)
Beanie Headphone (Not sure if it's still available)
My Mini's Lamp and PS Vita halo (Got taken away from me.)
Royal Crystal Crown
That's all for what my favorite rare items are. BUT to be honest my favorite rare items would be two things. Something you worked hard on to get and items that aren't available anymore. Those two are my favorite rare items.
I like threads like this, it reminds me of some good fun times over the years, and seeing all the items again. Some I missed out on, like the pants with the buckle and the chamber apartment, while others I was lucky to enjoy, like Xi.
For me, my favorite and most rare item to me is one of my newer ones, my Casino Roulette Winners jacket, which due to the writing on the back makes it the only one in Home, something i never though I would ever win.
Other favorites and rare items of mine are my Star Trek uniform (only available during a 2wk window at the end of 2009), my diamond EA poker bracelet and my RLS tracksuit (not so much the jacket, but I love the pants).