Wave is one of three infamous magical weapons introduced to Dungeons & Dragons in the 1st edition Advanced Dungeons & Dragons module "S2: White Plume Mountain". Alongside its siblings Blackrazor and Whelm, this weapon has managed to make an appearance in every single edition of the game, from 1st through to 5th, an honor that can't be shared with their oft-forgotten sibling, Frostrazor.
Crafted to honor a particular sea god (which one varies depending on edition), this enchanted trident has a lot of powers and has varied quite considerably over the editions.
When it appeared in 1st edition, in the infamous "giant crab in a safe bubble in a sea of boiling water" chamber, Wave was an intelligent True Neutral trident +3 with 14 Intelligence and 20 ego, determined to convert everybody to worship of its patron sea god (with Poseidon suggested as the default). This version of Wave had the combined powers of a Trident Of Fish Commanding and a Trident of Warning, possessed the ability to find water, granted its bearer the ability to breath water and act underwater, could function as a Cube of Force, and one final power: Dehydrate. On a to-hit roll of 20, it sucked vital fluids from the victim's body, causing them to take first the initial damage, and then to halve their remaining hit points.
In 2nd edition, Wave was moved outside of White Plume Mountain, hidden in the possession of Thingizzard, the Witch of the Fens. This version of Wave, now a Neutral Evil trident +3, was as smart and egotistical as ever, but had lost its proselytizing nature: now, all it cared about was staying the hell out of Keraptis' hands. It retained its Dehydrate power, unchanged from 1st edition, and combined the powers of a Trident of Fish Command with a Trident of Warning, although it had learned to affect swamp creatures as well as water creatures. It could also function as a Cube of Force, with 9 charges usable per day. Finally, it could grant the bearer Water Breathing and a swimming rate of 15 once per day.
The 3.5 version of Wave, a Weapon of Legacy, was covered in the "White Plume Mountain Revisited" adventure, a free upload done by WoTC, but now lost with their old website. Luckily, /tg/ gets shit done and tracked the stats down. Wave the Weapon of Legacy is, initially, a +1 trident that can only be wielded by someone of any Neutral alignment and with a BAB of +2. To unlock its full powers, you must complete three ritual trials: Mastery Over Sea (defeat an aquatic subtype creature whose CR equals or exceeds your level), Raise The Asterian (find the sunken shipwreck of the Asterian and bring its figurehead back above the waves), and Reverence to the Sea Queen (seek out Thunderforge Island, enter its temple to the Sea Queen, and perform an 8-hour rite of worship in her honor).
Once this is done, Wave starts to activate its powers. In addition to increasing in general strength, becoming a +2 trident at level 11, a +3 trident at level 16, a +4 trident at level 18 and a +5 trident at level 20, it unlocks a bevvy of special powers.
- As a 5th level weapon, it gives you the stupidly-named "Warning" ability; you can use a standard action to sense the presence of all aquatic creatures within 60 feet. Also, you ignore the damage reduction of any creature with the aquatic subtype.
- At level 8, you gain a permanent Water Breathing (CL10) effect so long as you are holding Wave.
- At level 10, Wave awakens and becomes a sentient weapon with Int 16, Wis 10, Cha 16, and Ego 10 (12 at llth level, 14 at 17th level). It has hearing and darkvision in a range of 60 feet.
- At level 13, it grants Underwater Vision; when underwater, you can see five times father than the prevailing water & light conditions would normally allow, and ignore the miss chance when attacking invisible creatures in the water.
- At level 15, Aquatic Allies lets you summon an Elasmosaurus, Large Water Elemental, Adult Tojanida, Orca Whale, Ichthyosaur or Large Monstrous Crab once per day.
- At level 17, Fish Command lets you make a Charm Monster spell (CL15, DC is the higher of 16 or 14 + your Cha modifier) 3/day that only targets creatures with the aquatic subtype.
- Finally, at level 19, it gains the Dehydrate power, which lets it cast Horrid Wilting (CL15, DC is the higher of 22 or 18 + your Cha modifier) 1/day.
In 4th edition, Wave was upgraded to the role of Paragon tier artifact weapon, located in The Plane Below, a sourcebook on the Elemental Chaos. This version of Wave is explicitly devoted to the goddess Melora and her exarch Sekolah, and many of its powers key off of facing down "heretics' (aquatic or elemental creatures that do not worship either Melora or one of Melora's exarches).
It is a +3 magic trident that does increased critical damage (+3d10) against heretics, grants the bearer a swim speed equal to their land speed, prevents them from being surprised by heretics, and has an Encounter power that lets them, as a minor action, ignore cover and concealment when attacking heretics until the end of their next turn. As you've probably figured, Wave appreciates if its bearer worships Melora or one of her exarches (+2 Concordance) and is gladdened whenever you slay a heretic (+1 Concordance per day). It's angered if you spare a heretic (-1 Concordance), outraged if you attack one of Melora's own aquatic/elemental servitors (-2 Concordance) and infuriated to be wielded by a heretic (-4 Concordance).
When Satisfied, Wave grants its bear the Aquatic subtype and lets them grant all allies within 10 squares the Water Breathing trait until the end of the encounter. When Pleased, it becomes a +4 weapon, deals +1d10 damage against heretics, and prevents you from being flanked by heretics. On the other hand, when Unhappy, you lose your protection against being ambushed by heretics, and when its Angry, you lose your swim speed and it downgrades to a +2 weapon. If at least Satisfied when moving one, it leaves its bearer with a permanent Swim speed equal to their land speed.
Finally, the 5th edition rendition of Wave appears in the Dungeon Master's Guide. This sentient (Int 14, Wis 10, Cha 18, hearing & darkvision out to 120 feet) +3 trident can only be wielded by someone sworn to a sea-god. It retains its Dehydrate ability, now manifesting as the victim of a critical hit taking Necrotic damage equal to half of their hitpoint maximum, and still functions as a hybrid of Trident of Fish Command and Weapon of Warning. It can act as a Cube of Force when called upon, and bestows the benefits of a Cap of Water Breathing on its wielder. Finally, it can Speak With Animals to all aquatic creatures, and use its telepathy to involve its wielder in the conversation.