ACTUALLY do not get to late game with these. They keep on scaling an really never fall off. Master Yi is fairly self-explanatory, AKA Master right click he just wins after the 40 minute mark. Kindred is similar to an ADC in a lot of ways and has high damage output along with a ult that prevents her from dying late game. As long as Twitch gets a few successful ganks early game, he will scale similar to Yi. Fiddlesticks has a great AOE ult that pairs really will with Zhonya's. Karthus has very high damage output and and a global ult. Even though he is very squishy, if you kill him his passive will punish you very hard.
Relevent all throughout the game
These are relevant picks all throughout the game. Even though they might not be as strong as early/late game champs at those selective stages of the game it doesn't mean they're weak at those points. My first pick for this is Jax, Jax is a scaling bruiser who can take 1v1 skirmishes very well early game. Lilia has high scaling damage output and good range all throughout the game. Sylas and Nunu are truly early game champs but have powerful ults and CC to carry them into the late game. My most controversial pick here is Evelynn. While most people believe that she is very weak early game, I strongly disagree. Even though Eve can't take many fights early, she is a very fast farmer and has high-gank potential even pre-6.
Mid game Assassins that fall off
These are mostly assassins that powerspike at level 6 but continue to fall off afterwards. Volibear and amumu aren't assassins but I'd like to put them here as they are meta mid game champs. Kayn doesn't technically powerspike until form but both of his forms fall off after ~4 items. Nocturne reaches a serious powerspike at 6 because pre-six he has minimal gap closers. Kha'zix receives serious damage output at level 6 but is weak late because of his low health. Ekko practically gets a second life at level six because of his Ulti.
Will probably steal you buff
These are junglers who try to get you out of the game really early because they don't scale very well. For example, Shaco has a high chance of using his Q to teleport over the wall and kill you. A jungle that is really focused on counterjungling is Udyr because he ganks are generally weak. Vi's Q allows her to easily travel through walls, making her a great invader. Warwicks sustain on his Q allows him to vertical jungle almost every game. Rengar and Xin Zhao can travel over walls if they have vision on the other side. REMEMBER: if you are playing against this type of jungler place control wards.
These are champs that can clear their jungle while taking minimal damage. Graves is a good pick here, as one of the best kiting champs he can kite out camps with his ranged autos. Hecarim, Olaf, and Zac all have forms of healing and area damage. The healing provides sustain while the area damage allows them to take swarm camps such as krugs or raptors. Rammus has tankiness combined with aoe damage on his Q allowing him to clear camps with staying healthy.