This is not a comprehensive list, but I will add to it as I find more toys! Pets and cardgame items are not included.
If you have a suggestion to add to the list, I'd love to hear about it!
Orb of Deception
- a BoE world drop in the 50-60 range, often seen from Blackrock Spire raid bosses and Zul' Gurub. Gnomes/Tauren, Humans/Orcs, Dwarves/Trolls, Draenei/Blood Elves, Night Elves/Undead. It's a permanent item.
Orb of the Sin'dorei
- heroic Magister's Terrace drop, off of any of the bosses. It's a permanent item.
- a random drop from the weekly Frenzyheart "Ripe Disgusting Jar," and probably the only interesting drop you can get out of it. It's a permanent item.
Iron Boot Flask
- purchased in Storm Peaks using Relics of Ulduar. Required for the But I'm on Your Side! achievement :) It's a permanent item.
Rituals of the New Moon
- an offhand item crafted by inscriptionists, the click-use is awesome :D I've seen large gray wolves, as well as the "coyote color" sandy wolves. Yes, you can do the ghost-wolf puppy dance while shapeshifted :) The recipe itself drops off of mobs in Silverbrook in Grizzly Hills. It's a permanent item.
Gordok Ogre Suit
- craftable by leatherworkers or tailors who have completed the Gordok Ogre Suit quest in Dire Maul. The dance is the same as moonkin :) This is a single-use item.
Super Simian Sphere
- an epic BoP trash drop from raids/heroics in Northrend, and a few mobs around Icecrown/Storm Peaks (such as the Captive Vrykul in the mines). Contrary to what most would assume, this is not a cardgame item (far as I am led to beleive!). It's a permanent item.
- dropped by Terokk in Terokkar forest. Summoning him requires a time-lost offering, which in itself requires a bunch of scrolls and killing his smaller minions. Farming this trinket will probably require several summons, as well. It's a permanent item.
- random potions in yellow-green bottles that spawn on the ground in the Underbelly sewers of Dalaran, these have a chance to proc one of several effects: Wasp, everyone else is a human mage, and Tuskarr (with +50 fishing).
Magic Eater fish
- fishies caught in the Underbelly sewers of Dalaran. They can proc any number of buffs when you spend time eating them, including miscellaneous stat buffs (crit/stam, haste/stam, AP/stam, SP/stam), or turn you into a green whelpling, mini basilisk, or cockroach!
- created by alchemists from Pygmy Suckerfish or attainable in the Dalaran fishing daily reward bags, this oil is used to make flasks of pure mojo, guru's elixir, potions of speed and wild magic, and to turn you into a little voodoo gnome when you drink ~4 of them straight!!
- fished from the Wailing Caverns in the Barrens, eating this fish raw can proc one of several effects: small instant heal or hot, +5 spirit, a short nap, shrink size + stam/str, and "Party Time!" which will cause you to do random emotes for 2 minutes. You can use this fish as a reagent for making Elixir of Giant Growth. You can also cook this fish instead, resulting in the next toy...
Savory Deviate Delight
- Flip Out! Consuming this fish will turn you into a human pirate or ninja!
- Purchaseable from a vendor, though you must do a questline to make this available for purchase. Starts and ends at Marin Noggenfogger in Gadgetzan, Tanaris. Drinking this potion can result in a featherfall buff, skeleton shapeshift, or shrink you!
Don Carlos' Famous Hat
- drops off of Don Carlos in heroic Old Hillsbrad. He paths along the road on horseback, his coyote following behind. It's a permanent item.
- a random drop inside the Dalaran fishing daily bag. All it does is spin you in place: a toy for the really, really easily amused. There is one trick you can perform with this item, however: if you use it while falling, it will momentarily slow you, resetting your fall distance. Used carefully, it can prevent a fall death! It's a permanent item.
Tiny Green Ragdoll
- purchased from the toy shoppe in Dalaran. Permanent item, 30-minute cooldown, it's a fun little ragdoll you can place on the ground. It surprised me that this is not a single-use item given its cheap price! I sometimes use it like a smoke flare, to mark a location on the ground (for tanking positions, etc).
Toy Train Set
- CHOO CHOO! purchased from the toy shoppe in Dalaran. It's a permanent item.
Wind-Up Train Wrecker
- CHOO CH-BOOOOOOOM. Tired of the train spam? Let loose this little robot and let him tear it up! It's a permanent item.
Zippy Copper Racer, Trusty, & Heavy
-single-use item from the Dalaran Toy Shoppe. Vroom... but short-lived :( Only difference between the 3 is their appearance, to tell them apart when racing with friends.
Grindgear Toy Gorilla
- another single-use toy.
Heavy Leather Ball
- crafted by leatherworkers. Click the ball, throw to friend. Yay!
Paper Flying Machine
- simple little fly-around toys that whiz through the air, akin to the balls and the Happy Fun Rock. They are a conjured item, thus will disappear after 30 minutes, so you will have to replenish them. Can be purchased from the Dalaran Toy Shoppe.
Happy Fun Rock
- drops out of Dire Maul, works exactly like the leather ball/flying machines. It's a permanent item.
Archmage Vargoth's Staff
- click to bring forth your Archmage buddy! It's permanent, as long as you don't turn in the quest. He'll flex and laugh and wave at you, if you emote at him.
Dartol's Rod of Transformation
- an alliance-only quest item from Ashenvale, though it is now limited to only being useable within a small area of the zone, unfortunately. You used to be able to use it anywhere, and most alliance players kept the item in their bags permanently to play around with when bored!
Romantic Picnic Basket
- a drop from the Valentine's hourly gifts, this permanent item has a 3-minute cooldown.
Crashin' Thrashin' Racer
- a special item from the 2008 Winter Veil gifts.
Brazier of Dancing Flames
- Summer Fire Festival item, will turn your into a firey draenei-lady when you /dance with it!
- a relic from the WotLK release event, it was a random drop from the undead mobs that spawned around Azeroth. If you do not have a pet out, a ghost figure will appear and follow you around! You also get the "haunted" debuff. These are not BoP, and can be tossed around like the leather ball/rock/etc, though they are so rare that few if any people actually play ball with these mementos!
- Hallow's End 2008 BoP item, this dropped off of the special boss in Karazhan in the one week (two instance resets) of the holiday. Few classes can use two-handed axes, but it's definitely good for a giggle to jam out!