Here are the top 5 champions for each role according to champion.gg. Some of this stuff is not too surprising and some is...pretty surprising.
Top
Graves -- tanky for a marksman with even better damage, can go in any lane because of his tankiness
Pantheon -- Thunderlords helps him early, new AD itemization helps him late
Quinn -- marksman damage, extreme mobility
Malphite -- everybody does physical damage, Malphite is natural predator
Nautilus -- ??? I guess he's one of the purest tanks and has some mobility with Q
Support
Janna -- best disengage/defensive support
Blitzcrank -- DA HOOK
Nautilus -- tons of CC, some mobility
(Taric -- but very low play rate compared to the others)
Sona -- strong laner with short-range poke and sustain
Leona -- best hard engage support?
Mid
Lux -- going
Talon -- AD itemization is good, AP itemization not so good
Corki -- does mixed damage with everything, so he can do sustained damage and still force enemy to itemize MR
Ahri -- just all-around strong with burst, mobility, and one of the best pick CCs
(Morgana -- but very low play rate)
Zed -- see Talon
Jungle
Udyr -- lots of sources of movement speed, Runic Echoes helps him burst
Graves -- see top
Fiddlesticks -- pretty low play rate, but Runic Echoes makes him more effective
Volibear -- juggernaut, good ganks, can get movement speed easier
Amumu -- because solo q
ADC
(Lots of low play-rate champs. Graves, Quinn, Twitch, Ashe all make appearances with very low play rates)
Corki -- see mid
Ezreal -- blue build is very strong if you can wait 30 minutes to build your first combat item
Miss Fortune -- Thunderlord's helps her, good laning and ult great in teamfights
Kalista -- hippity hop
Jinx -- teamfight hyper carry
Note that this is platinum and above, solo q only.
Top
Graves -- tanky for a marksman with even better damage, can go in any lane because of his tankiness
Pantheon -- Thunderlords helps him early, new AD itemization helps him late
Quinn -- marksman damage, extreme mobility
Malphite -- everybody does physical damage, Malphite is natural predator
Nautilus -- ??? I guess he's one of the purest tanks and has some mobility with Q
Support
Janna -- best disengage/defensive support
Blitzcrank -- DA HOOK
Nautilus -- tons of CC, some mobility
(Taric -- but very low play rate compared to the others)
Sona -- strong laner with short-range poke and sustain
Leona -- best hard engage support?
Mid
Lux -- going
Talon -- AD itemization is good, AP itemization not so good
Corki -- does mixed damage with everything, so he can do sustained damage and still force enemy to itemize MR
Ahri -- just all-around strong with burst, mobility, and one of the best pick CCs
(Morgana -- but very low play rate)
Zed -- see Talon
Jungle
Udyr -- lots of sources of movement speed, Runic Echoes helps him burst
Graves -- see top
Fiddlesticks -- pretty low play rate, but Runic Echoes makes him more effective
Volibear -- juggernaut, good ganks, can get movement speed easier
Amumu -- because solo q
ADC
(Lots of low play-rate champs. Graves, Quinn, Twitch, Ashe all make appearances with very low play rates)
Corki -- see mid
Ezreal -- blue build is very strong if you can wait 30 minutes to build your first combat item
Miss Fortune -- Thunderlord's helps her, good laning and ult great in teamfights
Kalista -- hippity hop
Jinx -- teamfight hyper carry
Note that this is platinum and above, solo q only.