Magic Missile is a basic projectile attack that costs nothing to use and deals decent damage. Higher level spells do more interesting and powerful effects, but MM can be a useful component of any Wizard build.
Magic Missile is basically a Firebolt that deals Arcane Damage. In early levels, Magic Missile might be the Wizard's bread and butter. Using this skill fires a small purple projectile that moves across the screen in a straight line and at a fairly fast pace, and it can be cast repeatedly without any cooldown or resource cost.
When an enemy dies at the hands of an Arcane spell, a purple glow is left on the corpses.
This was the default ranged spell at BlizzCon 2008, but with Arcane Orb and Electrocute available right from the start in 2009, Magic Missile was hardly touched. It didn't seem to have changed in function since 2008.
At BlizzCon 2010, Magic Missile was one of the Wizard's starting skills, and a very useful one, according to Flux:
The level five MMs were quite powerful, capable of killing almost any normal monster with a single shot. The casting rate wasn’t that fast though, which was good and bad. Good because you could cast MMs forever, since they weren’t fast or expensive enough to deplete your Arcane Power. Bad because I wanted to kill faster. Faster!
Skill tiers were removed for the July 2011 Press Event, allowing skills to unlock steadily from levels 1 to 30. Consequently, all skill levels were adjusted and Magic Missile became a level 1 skill.
The Diablo III Beta started in September 2011, and while it ran, all of the skills continued to undergo extensive iteration. Skill changes varied from changing the levels the skills are unlocked, to changes in resource cost, damage, and even function. A few skills were removed altogether, and a few new ones were added. Also, the entire skill system received an overhaul with the Beta Patch 13 update in February 2012, with physical runes replaced by rune effects that automatically unlock at various levels for the different skills.
Magic Missile remained at level 1 when the beta started. Flux tried it out again, and reported on it:
Naturally, the base version of Magic Missile isn’t all that powerful. It’s great for single targets, and has nice range and quite respectable damage, but with just a single projectile per cast the Wizard can not keep up with fast spawning enemies, and MM isn’t much good for bosses either. I’m not just estimating about that either, since I actually put it to the test. MM was fine for 95% of the beta areas, including the lower levels of the Cathedral, but when I got boss packs, or set event areas of summoners, there were too many fish for my skillets, and I got overrun and had to retreat or use other skills.
With the Beta Patch 8 of December 2011, all signature spells became free to cast at any level. With the Patch 13 changes, Magic Missile was classified as a Primary skill (but remained at level 1).
In Diablo III, Blizzard seems to have gone back to games like Dungeons & Dragons for inspiration. A spell called Magic Missile is a staple low-to-mid level magic bolt in the traditional pen & paper RPG. The Magic Missile also increases number of missiles, as does the original. Wikipedia describes D&D Magic Missile like this.
A bolt of pure energy from the caster's fingertips, which in most editions of the game never misses its target unless prevented by magical means. The number of bolts one can cast increases with practice.