Dungeons & Dragons 5e
(Tasha’s Cauldron of Everything p.66) These sorcerers have been marked in some way by an aberrant mind and it has left its mark in so many ways, in particular by allowing the use of psionic powers. They can communicate with another through telepathy, cast psionic spells, have defenses against mental attacks, change their bodies to be more like their master’s with its horrifying inherent abilities, and can create a teleportation implosion. These are definitely one of the creepier Dungeons & Dragons 5th edition sorcerers, especially when their skin covers itself in mucous while they slide their bodies through the tiny gap under a closed door.
(Tasha’s Cauldron of Everything p.68) These sorcerers have a connection to the force of order, likely through the modrons of Mechanus. They are able to neutralise advantage and disadvantage, create defensive shields, increase their abilities, and repair/heal creatures and objects around them. Without question, these are the most steampunk of the Dungeons & Dragons 5E sorcerers.
(Xanathar’s Guide to Everything p.50) Divine Soul sorcerers have been touched by a divine being of some sort. They are able to learn divine spells, which are usually only available to clerics and druids, as well as the typical arcane spells which most sorcerers know, which is quite nice. These sorcerers can roll 2d4 to add to a failed saving throw or attack roll, they can spend a sorcery point to reroll one or more healing dice from a spell the sorcerer or someone close by cast, they can grow wings and fly, and they can heal themselves with a blast of healing when they are doing badly.
(Player’s Handbook p.102) These sorcerers have a link to a dragon in their past or their ancestry. As a result, they gain additional hit points, they have a covering of scales which increases their unarmored AC, they grow wings which they can use to fly, they do extra damage when casting spells using the damage type of the dragon which they are connected to, they can use sorcery points to gain resistance to that same damage type temporarily, and they cause awe or fear like a dragon.
(This is an unofficial Dungeons & Dragons 5th edition subclass from the Tal’Dorei Campaign Setting p.103) The Runechild sorcerer has received their magic from the arcane, which manifests in the form of runes. These sorcerers are covered in runes which activate when sorcery points are used, and which can then be discharged to absorb damage, give advantage to their STR, DEX, or CON skill checks, reveal hidden magic around them, breach the immunities or resistances of a foe, or to turn the sorcerer into a magical being with the ability to fly, resistance to spell damage, a higher spell save DC, and the ability to heal when they cast spells.
(Xanathar’s Guide to Everything p.50) Shadow Magic sorcerers have been touched by the Shadowfell at some point. They have darkvision to 120 feet, and get the darkness spell for free and can cast it using either a spell slot or with sorcery points (and can see through the magical darkness if sorcery points were used). When these sorcerers drop to 0 hit points they can roll a CHA saving throw to instead drop to 1 hit point, they can call a hound of ill omen to target a creature, they can teleport between shadows, and they can even transform themselves into a shadow.
(Xanathar’s Guide to Everything p.51, Sword Coast Adventurer’s Guide p.137) The Storm Sorcerers get their magic from the element of air. They are fluent in primordial, they can fly without provoking opportunity attacks, they are resistant/immune to lightning and thunder damage, and they deal extra thunder or lightning damage to nearby creatures whenever they cast a spell using either of those two damage types. In addition, these sorcerers can control the weather in subtle ways, they can use their reaction to strike their attacker with lightning damage when the sorcerer is hit, and they can choose several creatures to fly with them when they fly.
(Player’s Handbook p.103) These sorcerers arise from the forces of chaos, and their magic is shaped by that. Every time they cast a spell they roll 1d20 and if they roll a 1, they roll on the wild magic surge table to see what chaotic side effect happens- some are good, some are neutral, and some are bad. In addition to that delightfully chaotic effect, wild magic sorcerers also can gain advantage on a roll, after which at any time the DM may ask them to roll on the wild magic surge table to regain that ability. They can also use sorcery points to add or subtract 1d4 from another creature’s roll. The chaos which emanates from this sorcerer will almost certainly upend any plans which your party makes on a regular basis in the absolutely best ways possible.