The Staff of Boccob: This staff combines the features of a staff of the magi, a staff of power, and a +5 defending quarterstaff.
In 1e/2e, it's called the Staff of the Archmage. It is still a staff of the magi, and instead of a staff of power, it has the powers of a wand of conjuration. Of course for Boccob, a staff is just for flair. His best mode of attack is casting the disc of concordant opposition which blasts foes into nothingness.
Jenevier is cool and all, but in AD&D Ehlonna has no named bow, but her bow doesn't matter because she never misses with one. Known for her magic quivers, Ehlonna carries +3 arrows, arrows of slaying, a +4 dagger, and a +6 defending longword. Damn, she is ready for battle!
Agony: This is the weapon of Erythnul, god of slaughter. Agony is a +5 chaotic, unholy, morningstar, whose head has a demon's face on one side and a boar on the other. It also has the unique "frightful" power. It makes an unearthly wailing noise whenever the wielder attacks. This is a sonic, mind-affecting fear effect.
Strangely in AD&D, Erythnul's stone-headed mace is not a magic item, but it does have a fear inducing wail. Brutal enough I guess.
Traveler's Friend: This is the walking stick of Fharlanghn. It serves as a +5 defending, speed quarterstaff.
In AD&D Fharlanghn has an iron-shod staff of no particular name or note, except that he never misses with it. His main mode of combat however should be the Oerth Disk, which has so many functions I could do a whole post on it alone.
Heresy! As we all know, in AD&D the invincible one uses a battle axe. His +4 battleaxe has no name though, and interestingly it can shrink to 1/20th size at command, so he can hide it on him while in disguise.
Executioner: This is Hextor, the god of war's "favorite" weapon. Executioner is a +5 lawful, unholy, ghost touch light flail.
Executioner is cute, but come on, a light flail is his favorite? In the original AD&D source, Hextor (who has 6 arms by the way) carries two spiked bucklers, a +2 fork, a +3 scimitar, a +3 morning star, and yes, a +2 flail. None of them have names, so I guess he breaks out Executioner on special occasions.
Kelmar: This is the famous sword of Kord, god of strength. Kelmar is a +5 dragon bane greatsword. The sword is intelligent, and chaotic good. It's special purpose is to slay lawful dragons.
In AD&D, Kelmar is an "electrified" +5 intelligent sword that among many powers, does indeed slay dragons, with a vorpal quality. Snicker-snack!
Lifecutter: The only weapon carried by Nerull, god of death. Lifecutter is a +5 brilliant energy, keen, speed scythe. It resembles a gnarled staff of ebony with a curved blade of energy.
Okay Lifecutter is pretty spot on here, but the AD&D version is obviously nastier. It's just a +5 scythe, but it causes instant death on a failed save, among other side effects. Don't mess with the reaper.
Stormstouch: This is the staff of Obad-hai, god of nature. Stormstouch is a +5 defending, shock burst, speed, icy burst quarterstaff.
More heresy. Obad-hai's nickname is the Shalm. In AD&D he carries the Shalmstaff. This staff may not be as offensive minded as Stormstouch, but its a +3 quarterstaff that he can summon to his hand instantly, allow him to walk tirelessly without food or water, plus animals will not harm Obad-hai, and plants move out of his way. Shalmstaff wins.
Swiftstrike: The main weapon of Olidammara, god of rogues and music. Switftstrike is a +5 chaotic, keen, speed rapier.
In AD&D Olidammara isn't really interested in fighting it seems. His main item is a stringed instrument, the Kanteel of the Oldest and he has a bunch of defensive items. No mention of a rapier, much less any specific weapon.
Pelor is never really detailed in previous sources, so Sunscepter is a delicious addition to lore. Pelor isn't messing around either (unlike Hextor) by carrying a heavy mace. I'm surprised his mace doesn't have a light power though.
The Mace of St. Cuthbert: This famous weapon is a major artifact. It acts as a +5 disruption, holy, lawful heavy mace. It can cast searing light.
The Mace is a classic item, its been adapted in all editions. In AD&D, at its base, its a +5 mace of disruption that does 1 INT damage on a crit. Ouch! By the way, Cuthbert also totes a regular bronzewood cudgel that is +3 and does morningstar damage. Thwack!
Afterthought: This is side-weapon of the arch-lich Vecna, god of secrets. Afterthought is a +5 ghost touch, wounding, unholy dagger.
Vecna is best known for his Eye and Hand of course. He is an archmage that can cast virtually any spell in the PHB, so why does he need a weapon? I guess to toy with mortals? Afterthought is just that, and for that, I like it!
Discretion: This weapon is carried by Wee Jas, goddess of magic and death. Discretion is a +5 lawful. ghost touch, keen dagger.