Assassin, Fighter, Mage, Marksmen, Support, Tank

Nah.

It misses way too much nuance.

How about...

Blaster, Controller, Utility Fighter, Striker, Assassin Juggernaut, Vanguard, Warden

Blaster: Lower mobility, heavy focus on burst damage often with a strong AoE component. Controller: Sacrifices raw burst and/or range for potent CC and zone denial. Utility: Sacrifices kill potential for the ability to powerfully augmented allied champions.

Fighter: Strikes a balance between burst and sustained damage. Moderate mobility with the ability to go in, but rarely the ability to get out. Striker: Mobile champions with heavy focus on sustained damage. They typically mitigate damage through avoidance rather than resistance. Includes nearly all the champions flagged as 'Marksmen'. Assassin: Highly mobile champions with heavy focus on low to moderate cooldown burst damage.

Juggernaut: Durable champions with close range hard CC or moderate range soft CC. What they lack in mobility they make up for with raw damage. Vanguard: Mobile, durable champions with lock-down crowd control. Ideal initiators. Warden: Moderate to low mobility champions with potent CC and/or protective abilities and high durability.

And of course many champions are a combination of two (or more in some cases) categories.