It all really depends on your level of play (low level, unranked, low elo, high elo, smurf, etc.) Here are my recommended Champions for each role.
Top: Fiora (her W - Riposte is the only skill in League of Legends that can literally negate all other skills, stunning if she negates a form of cc), Riven (considered to be one of the hardest Champions in LoL, only one player has truly mastered her)
Mid: LeBlanc (outplay queen), Zed (outplay king), Ahri (play-making queen)
Jungle: Rengar (stealthy, bursty champ capable of 1-shot killing anyone without a Thornmail or Armor items), Kha'Zix (read Rengar desc.)
ADC: Kalista (do not soloq with her, half her kit is disabled without her Oathsworn) Jhin (heavily reliant on skillshots and his 4th auto), Ezreal (extremely poky yet entirely skill-shot reliant, Kalista can decimate him)
Support: Leona (one of the best Supports, having the best gank-setup at Level 3 with a root-stun and a teamfight-changing ulti) Soraka/Sona (heals for days and fight-changing ultis), Alistar (the tankiest Support in LoL with his ulti, and a hard engage/disengage kit)
If you have Leona/Ashe bot, Ahri mid, and Fiora, Riven, or a toplane with CC top, Master Yi is a very excellent Jungler to use, having amazing synergy with CC-heavy teams. Also Talon is excellent as a mid or adc (I've seen a Yasuo ADC in LCS)