What are all the races of elves?

Devor about summed it up. However, the elves of Tolkien are rooted in (mostly Norse) mythology, and elf-like races (sort of) turn up in other mythologies.

This is from memory, so likely a few issues:

Norse elves have two broad categories: Alfar and Dock-Alfar. Collectively the Huldrefolk or hidden folk. Alfar are...reasonably close to the elves of Tolkien and other modern authors. Dock-Alfar were more sinister, occasionally dwelt underground, and were superficially like the Drow.

In Celtic mythology, elves were termed 'Sidhe,' and there were several types, many not exactly friendly to humans. A bit closer to elves as currently viewed in fantasy works.

In South Asian mythology we have the Gandharvas (male) and the Aparusu (female). The former were divine musicians, the latter dancers, yet both could be termed elves of a sort.

 

It really depends on what your goals for the game are.

Are you styling it after other games? World of Warcraft uses Blood Elves and Night Elves. A search for elf and Dungeons and Dragons turns up a much longer list of subraces than I expected: Elf (Dungeons & Dragons) - Wikipedia, List of Dragonlance creatures - Wikipedia.

Since elves don't exist, you have a fairly free hand and can create whatever elves you like. People are going to bring some preconceptions to the game when they hear the word elf, so that's your only real limit or consideration.

 

Don’t forget the kitchen sink elves!

But seriously though, it’s completely up to you if you use elf races, or even elves at all. Just don’t forget to add some original flair to them!

 

How about instead of making their racial traits what makes them unique, have their culture make them unique? Perhaps have normal elves, but they are industrious? Or perhaps they sail the seas in search of resources to bring back to their homeland?

 

Umbrals are a strange creatures. Lean and waifish, they only somewhat resemble Humans. Standing between 3 and 4 feet tall, their limbs are long and their fingers and toes end with razor-sharp claws. Their ears are pointed and turned downward and they have large liquid eyes that see perfectly in low-light conditions. They interact with shadow as easily as they breathe, using it to travel, to escape predators, or as a weapon in times of great need. They even clothe themselves in wispy garments fashioned of shadows. An industrious people, they dwell in narrow canyons or the deepest parts of the forest, places with a constant source of shadows. Though they are grim-looking places, they are places of enlightenment. They have libraries, academies, manufactories for all manner of things and their lives are very structured around the collective good. The society is a guild-based oligarchy; with the leaders of the guilds serving as advisors to the elected leader. To outsiders, their societal structure seems chaotic, but actually, it is well-ordered in seven year cycles. A ruler or guildmaster governs for only seven years, before they appoint a successor of the opposite gender.