The Best Weapons in Dark Souls 3
The best weapon in Dark Souls is the weapon you are best with. That smart-ass comment aside, some weapons have a lower skill floor, stronger movesets, and/or stronger attack ratings (AR) than other weapons.
You should expect to run into these weapons in PvP at a much higher rate than other weapons because they are perceived as unfair. Just remember that for most people, skill trumps stats in most cases.
The Weapons
The following list isn't necessarily ranked in order (for example, some people might like Butcher's Knife more than Drang Hammers), but generally speaking, the stronger weapons will be towards the bottom.
Butcher Knife (24/0/0/0)
A poorman's Fume Ultra Greatsword, the Butcher Knife has a unique moveset that heals the user with each attack (notable, but for the most part irrelevant). It scales A in strength until +10 when it scales S. Since it's found early in the game (and it's relatively light), it's great for strength builds until your preferred endgame weapon is found.
Drang Hammers (18/16/0/0)
Solid scaling with a good moveset, the Drang Hammers are a fantastic weapon for both PvE and PvP. The dual-wielded (two-handed) attack has a knockdown/stun that turns into a stunlock when it's properly timed. Best used when infused as a strength weapon (it scales A in strength when heavy-infused), it's still buffable with resin or rouge.
Gotthard Twinswords (12/18/0/0)
The Gothhard Twinswords have one of the fastest movesets in the game that still has reasonable range and damage. One of the only drawbacks is that it's found so late in the game that most builds need to level a different weapon early on or mule it to their new character from a friend.
Irithyrll Straight Sword (12/14/0/0)
Generally speaking, the straight sword weapon type is very strong in Dark Souls 3 (you'll find three of them on this list). The Irithyrll Straight Sword's moveset is solid, it's pretty light, quick, and one of the only relevant weapons with the frost auxillery (a weaker bleed that slows the enemy down and reduces stamina regeneration). Like the Butcher Knife, the Irithyrll Straight Sword is more of an early game weapon that you'll use until you are able to transition to a weapon with a stronger attack later on, like the next weapon...
Dark Sword (16/15/0/0)
The Dark Sword is basically a greatsword weapon disguised as a straight sword (that means there's very little reason to actually use a greatsword in Dark Souls 3, just use a Dark Sword instead); the stomp weapon art provides hyper armor. While it has a slightly smaller range, the Dark Sword is much faster and requires less stamina (and equipment load) to use. It scales well with virtually every infusion (S when lightning/crystal, A when heavy, B/B in when refined). The Hornet Ring also works with it due to the standard/thrust attack typing.
Washing Pole (18/20/0/0) and Uchigatana (11/16/0/0)
I'm lumping the Uchigatana and the Washing Pole together since they are pretty much the same weapon. The Uchigatana can be found earlier in the game, but most players will switch to the Washing Pole once it's available.
The Washing Pole has the longest range of all katanas, deals the second-most damage (behind the Chaos Blade) and can be buffed (unlike the Chaos Blade) but takes more stamina to use than other katanas. The increased stat investment should be irrelevant since most katana builds are quality builds instead of a pure dex build.
In PvP, the Washing Pole has phantom range where the wielder can hit the enemy even though (s)he appears to be out of range.
Estoc (10/12/0/0)
One of the most effective weapons in the game, the Estoc is an extremely fast thrusting sword. Although it doesn't scale all that well, the moveset's R1 spam is a miniature stunlock that lasts until the wielder runs out of stamina or the victim is dead.
Fire or deep infused Estocs have 330 AR (165 split between phystical and elemental) at +10 and are useful for PvE (especially early on in the game).
Anri's Straight Sword (10/10/0/0)
The speedrunner's favorite weapon, Anri's Straight Sword is easily one of the strongest weapons in Dark Souls 3 (especially when paired with Carthus Rouge on a luck build). At 40 luck (with 10 STR and 10 DEX), your AR is around 400. In addition to the high damage and fast attacks, Anri's Straight Sword is also blessed-infused, providing minor HP regeneration and 10% bonus damage against skeletons.
Oh yeah, and because it has a thrust attack, it benefits from the Hornet Ring.
Fume Ultra Greatsword (50/10/0/0)
Even with the harshest strength requirements in the game and a few nerfs, the Fume Ultra Greatsword is still a beast of a weapon. A STR build featuring 50 STR/14 DEX, will have 571 AR with a +5 Fume Ultra Greatsword.
Dragonslayer Greataxe (40/0/0/0)
Falling Bolt, the Dragonslayer Greataxe's weapon art, makes it arguably the best weapon in Dark Souls 3. At +5, it has a little over 500 AR split between physical (370) and lightning (136) before taking any stats into account (it scales C/E/-/D, for the record). Best used in a STR/FAI build, it's still potent for quality builds.
Final Thoughts
There are your ten strongest weapons in Dark Souls 3. If you're having a lot of luck with a weapon I didn't mention, let me know in the comments. The game has a lot of options and I'm sure I missed one (and here's to hoping that FROM Software improves the weaker weapons, like cestus/claws).