Am I the only one here who feels that Annie is a Mage/Assassin?

Pretty sure mages are known for their burst and stuns are a form of utility (which assassins lack).

Just because a champion can kill you quickly doesn't mean they are an assassin.

Certainly not an assassin. She can deal a lot of burst damage, but so can other champions who do not need flash to get in close.

Generally for a champion to be considered an assassin they need to have mobility in their kit, mages can deal comparable damage to assassins but may lack the tools to get close consistently. For an assassin flash is an additional option rather than the entirety of their options for getting close to the enemy.

Assassins: "Agile champions that close in and take out unsuspecting targets in the blink of an eye. However, they must pick their opportunities carefully since a high-octane offense comes at the cost of low defense and long waits between takedown attempts."

http://na.leagueoflegends.com/en/site/guide/roles.html

Annie has to walk up to you to press R. No escapes. No blinks. No tricks. Besides flash which everyone has, she just walks up to you. If just having damage on your ult makes you an Assassin then so are these champions:

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That Flash + Multi Stun of hers + AP melting is insane.

Nah she's obviously an assassin/mage.

Not an assassin, but if there were a role of low range AOE disintegrator-Annie would be there, with Nunu, Graves, Fiddle and probably Illaoi