Random power / super archetypes;
Bricks/Tanks/Armor - Colossus, Blok
Scrappers/Infantry - Wolverine, Timber Wolf
Mentalists/Psychics/Communications - Jean Grey, Saturn Girl
Blasters/Artillery - Cyclops, Lightning Lad
Control - Karma, Mirage, Light Lass, Projectra
Defense/Damage Prevention/Healing - anyone able to create force fields / defensive walls or heal others
Transport - Nightcrawler, Gates
Airborne - Angel, anyone with a Flight Ring
Skill-Based - Prodigy, Batman, Brainiac 5
Elemental Manipulation - Crystal, Terra, Mera, Elysion, Nightwind
D&D type games break them down to Healer / Buffer, Mage (ranged damage and utility and debuffing), Tank and Skill-Monkey.
City of Heroes went with Controller (crowd control like stuns and illusions), Defender (healing and 'buffing' and debuffing to prevent damage), Tank (take lots of damage), Scrapper (put out lots of damage), Blaster (ranged damage)
'Control' and Buffer/Debuffer/Healer roles are the least common in comics. Despite often being team characters, the majority of heroes are pretty 'selfish' power wise. Raven is a rare example of someone who is almost exclusively designed around roles not common to super-team heroes, being a healer, capable of 'controlling' an encounter by sending her soul-self out to paralyze someone temporarily, and a teleporter.
Many powers and types cross roles, and many individual characters have multiple roles. Superman is a flying tank who also can function as a blaster with his heat vision. Lightning Lad and Cyclops, on the other hand, are just blasters. That's all they do (unless Leadership/Command is added as another role!).