Wave Beam

The Wave Beam, named such for its wavy pattern and because it fires "wave energy", is a beam that Samus acquires in most games, with the exceptions of Metroid Prime: Hunters, Metroid Prime 2: Echoes, and Metroid Prime 3: Corruption (though she gains the Annihilator Beam in Echoes, the Volt Driver in Hunters, and both the Grapple Voltage and the Nova Beam in Corruption, which all share a few similar properties with the Wave Beam). It fires wave energy (often in the shape of a sine curve) that can usually go through walls.

2D series
In Metroid and Metroid II: Return of Samus, the Wave Beam generated a single bolt that moved forward in a sine curve and passed through walls. It was stronger than the other beams. It also acted as such in Super Metroid, as long as the other beams had been turned off, with the exception of the Power Beam, which could not be turned off.

In Metroid: Zero Mission and Metroid Fusion, the Wave Beam was a beam that could go through walls. In these games, it acted as a power-up to the normal beam(s) that Samus had acquired thus far. In Super Metroid, it could be added to any other combination of beams to make them go through walls and give them a waving trajectory, or be used alone, making a purple waving ball. In Metroid Fusion, it adds a "go through walls" effect to the already-acquired Charge, Wide, and Plasma Beams. In Zero Mission, it added a widening effect and a phase effect to whatever beams Samus has by that point (Samus could actually obtain the item without any other beams, but she could have the Ice, Charge, Long, and even Plasma beams by then, due to the game's non-linear nature).

In Metroid Fusion, this upgrade was possessed by the haywire robot B.O.X. This is the second to last beam achieved by Samus on BSL, before the Ice Beam.

Metroid Prime
In Metroid Prime, the Wave Beam takes on a different role. Here, it is one of the three "elemental" beams, it representing the element of Electricity. It is the first beam Samus achieves on her mission to Tallon IV. The Wave Beam does not go through walls. However, if the player is locked on to an enemy, the beam has a homing feature that can follow an enemy around until it hits. The Wave Beam is acquired after defeating a Sheegoth in the Chapel of the Elders, located in Phendrana Drifts. When fired normally, it launches three separate rounds that undulate inwards and outwards continuously with impressive homing capabilities. When charged, it fires a slower-moving single round that, when used on a few certain enemies, can cause a stunning effect. Its uses outside of battle include energizing Power Conduits and opening Purple Doors. It is the only weapon that can destroy the Pulse Bombu and the Scatter Bombu. On a related note, if the Wave Beam is used on an Auto Defense Turret or a Mega Turret, it reacts in a similar manner to a glitch in real-life automated turrets.

Also in Metroid Prime, the Wave Beam can also be upgraded with a Charge Combo called the Wavebuster. This allows Samus to fire a perpetual wave of electrical energy at an enemy, and like the normal beam it has a limited homing feature which doesn't require a lock-on, but its range is somewhat low. This attack uses up ten Missiles to activate and uses five Missiles per second when holding the fire button. Although it has an extreme ammunition cost with less damage-per-missile than the Super Missile, it deals damage at an incredible rate, making it valuable at quickly defeating enemies in a pinch.

Metroid: Other M
In Metroid: Other M, the beam fires three purple undulating shots at once, similar to in Prime. Other M's Wave Beam also has similar properties in the 2-d games; bypassing walls. However, it is only limited to "transparent and semitransparent" objects, such as glass.

It is authorized by Adam in Cryosphere, when Samus is being attacked by several Zebesians that she cannot counterattack due to being surrounded by glass walls and them being able to bypass it with their shots. All Zebesians seem to have a version of the Wave Beam.

Metroid manual
"The beams are wave-shaped and are stronger than normal beams. If you already have a long beam, the long beam will become a long wave beam."

1986 Manga
"This beam flies in a wave pattern and is more powerful than the normal beam."

Official Nintendo Player's Guide
"This is a powerful weapon. This beam travels like a wave, and destroys in all directions. Also, it has the power to penetrate and destroy obstacles."

Metroid II: Return of Samus manual
"The beam travels in a wave shape. It is a very powerful beam and has a wide range of effect."

Super Metroid manual
"The Wave Beam sends out a charge in a wavy pattern and pierces some obstacles."

Official Metroid Prime website
Weapon effect: Enemies enveloped in electrical energy.

Weapon range: 3 - 10 m

Weapon potential: Lethal

"Chozo Technology. Samus Aran uses the Wave Beam to fire powerful electric bolts from the Arm Cannon. Enemies struck by the Wave Beam's blast are enveloped in electrical energy for a few moments. The Wave Beam's electrical charge can also "lock-on" to its target to a limited extent."

Metroid Prime manual
"The Wave Beam fires three oscillating waves of energy. As with the other beam weapons, the Wave Beam is especially effective against certain enemies and can be powered up once Samus finds the Charge Beam. The Wave Beam also features a limited homing effect."

Metroid Fusion manual
"Shoot through obstacles with this undulating beam."

Metroid: Zero Mission manual
"This allows Samus to fire beams of energy waves that penetrate solid objects."

Zero Mission Samus Screen Data
"This beam, which is made up of energy waves, can pass through solid objects."

Metroid.com
"This beam passes through windows and other transparent objects. With added functionality comes added power - the Wave Beam also makes short work of many tougher creatures."

Metroid: Other M manual
"Adds the ability to penetrate transparent and semi-transparent objects. This powerful beam can also be shot as a Charge Beam."

Trivia

 * In Metroid Prime, the Wavebuster combo is especially useful for destroying a Sentry Drone in the Phazon Mines equipped with invisibility as Samus is unable to lock-on to invisible enemies and getting a direct hit can be difficult otherwise.
 * The Wave Beam Arm Cannon formation looks exactly like the Light Beam from Metroid Prime 2: Echoes, and the Nova Beam from Metroid Prime 3: Corruption.
 * In Super Metroid, the Wave Beam shares a similar sprite to the Energy Capsules.
 * In the New Play Control! and Metroid Prime Trilogy versions of Metroid Prime, sparks of electricity no longer appear on the Arm Cannon when charging. Theories suggest this may be due to the way this and other visual effects were programmed into the original game, making it impossible to reproduce the effects on the Wii alongside the new aiming system.
 * Normally, getting the Wave Beam in Super Metroid requires using the Grappling Beam. However, it has been found to be possible to wall jump to get the beam early.
 * The Wave Beam was slated to appear in Marvel: Ultimate Alliance along with Samus herself and many of her other abilities, though they were removed due to Nintendo not giving consent for her inclusion. The Wave Beam in Ultimate Alliance appears to be based off of the Prime iteration.
 * The Wave Beam has had an impact on the fanbase, as the Metroid Database's podcast is named after the Wave Beam, and it currently has three episodes.
 * In the first Metroid Prime, the symbol for the Wave Beam is a hand print with all of its fingers spread apart. Using the X-Ray Visor reveals that this is the configuration Samus uses to activate her beams.