Personally, full ad BRAD was so fun when he came out (yes even in his weak form) I went 13/2 as him.
full ad darius gets 1k damage crits with his W every 2 seconds, if they survive that you have the attack speed to reach 5 stacks of your passive and get 200+ bonus AD and your ult deals upwards of 1.5k true damage that you can keep recasting every kill.
regendinger start three regen beads, rush spirit visage, build ohmwrecker banner and zzrot, push three lanes at once while being horrifically tanky and having just enough damage and disruption to be obnoxious in teamfights
Something that everyone says is fun is full AP 
. Personally, I haven't tried her in a normal game, but she is busted in ARURF. She ends up being super tanky and packs a lot of punch. I go 
and i can survive the burst of an ap mage while one shotting them at the same time.
Another fun one is Full AP Malphite. That's busted in urf too.
AP Soraka. It's my go to off meta build, and it's super fun! 
That, or cinderhulk jungle poppy. It's fun, because of her shield passive that gives her a good clear, her w and e for ganks, her ult for disruption, and her q for jg farming.
AP nami mid is always a fun thing to pick up, they never expect to lose trades.
