I figured this topic should be started not only as a conversation piece but it could also help as a faq for newer players to see why the current players use the champion that they do. Personally I use a few champions based on who my team chooses but generally I stick to my main three:
1. Anivia: She has extremely strong abilities and deadly combonations if they are strung together correctly and on time. Anivia is one of the best creep farmers in the game after Lvl. 6 due to her Glacial Storm ability (I average anywhere from 120-170 creep kills per game). The final thing I like about Anivia is she holds her own and is tough to kill due to her Rebirth passive ability.
2. Ashe: I started out with Ashe as my first champion because I assumed a ranged champion would let me get the feel of the first few matches I played. She is easy to learn and is a solid creep farmer as well. After her movement is increased she is one of the most versitile characters in the game. She can take down opposing champions or be used as support for the tankier players with the Volley ability. The last thing I can say about Ashe is the "highlight reel" kills she can occasionally pull off with her Enchanted Crystal Arrow ability. The arrow has the abilty to fly across the map until it hits a champion so you can fire it from your base and get a kill in the enemies base which is a feel good moment for new players and pros alike.
3. Garen: I use Garen strictly when I want to hit something, alot. The damage this guy packs with his basic attacks alone is impressive let alone his ability to silence and increse movement and attack speed with one ability. Like Ashe, Garen is very versitile in the sense that he can be a fighting tank and creep farm with his Judgement ability where he spins for a second or two, damaging every enemy within range. Once he is ramped up with items Garen is tough to slow down.
If I had to pick a favourite champion I would probably say Anivia just because she is difficult to learn and I have learned to handle the Cryophoenix pretty well. Her abilities rock and she is one of the most unique looking champions in the game so I recommend giving her a try, especially if she is free to play at some point.
Thats my champion, and I would love to hear other players picks and why they enjoy using them. The possibilities are really endless.