AP Ezreal (small handicap)
Not 100% viable for a ranked game, but you can still carry (or crush) your friends with this. This is definitely a late game build but once you get your lichbane, your damage output is awesome. Your w and r are your main damagers. q does very well once you get lichbane. Even though e does a lot of damage, you still usually want to save it for escaping.
AP Varus (big handicap)
Your w and r make this viable. Your R can do a ton of damage and your w makes your basic attacks deal 1/4 of your ap as magic. also, your other abilities can do up to 50% of their health as magic if you build him heavy ap. So, you want to auto attack a target 3 times then use a spell. This will give you your max damage from w.
AD Annie (small handicap)
The only reason this isn't totally awesome is because her attack speed is too slow. Her spells still do good damage. She has an aoe stun. She has good range. Like it. If you are playing with some noob friends, you don't need a defensive item. You have good range and you know how to position.
Difficult to pull of because he is not ranged. However, his ult makes him hard to kill. He can heal, he has good cc which makes him good at 1v1. Really fun, unless it goes bad. Then it sucks.