Damage numbers for all weapons

There is This Overwatch Damage Spreadsheet with numbers for most weapons and abilities.

In case the link goes down:

Genji
Shuriken                 |105 (35x3)
Swift Strike (Impact)    |30
Bleed                    |29
Dragon blade             |120

McCree
Peacekeeper              |70
Fan Fire                 |420 (70x6)
Deadeye                  |100-OHKO; 50% = ~300

Pharah
Rocket Launcher          |120
Splash                   |13-80 (up to 40 v self)
Concussive Blast         |1
Barrage                  |~40/blast, Total = 2500+

Reaper
Hellfire Shotgun         |Up to 140
Death Blossom            |510 (~35x2/sec)

Soldier: 76
Heavy Pulse Rifle        |17
Helix Rockets            |120
Splash                   |13-80 (up to 40 v self)

Tracer
Pulse Pistol             |6
Pulse Bomb               |450

Bastion
Assault                  |20
Siege (turret)           |15
Tank                     |190

Hanzo
Storm Bow                |23-125
Sonic Arrow              |23-125
Scatter Arrow            |Up to 450
Dragonstrike             |~43/tick

Junkrat
Frag Launcher            |120 (40 v self)
Frag Splash              |40-80
Concussion Mine          |120
Steel Trap               |80
Rip Tire                 |600
Total Mayhem             |Up to 300

Mei
Blaster (channeled)      |2.25 / ammo
Alt-Fire                 |75
Iceblock                 |150 Heal
Icewall                  |500 health/pillar
Blizzard                 |97 (3.88 x 25 ticks)

Torbjorn
Rivet Gun                |55
Alt Fire                 |24-100
Forge Hammer             |75
Turret                   |14
L3 Turret MIssiles       |~70

Widowmaker
Widow's Kiss (auto)      |13
Widow's Kiss (scoped)    |20-80-150

Lucio
Sonic Amplifier          |80 (20x4)
Knockback                |25

Mercy
Caduceus Blaster         |20
Caduceus Staff

Symmetra
Photon Projector         |7
Average over 6s          |13.5 dmg/shot or 100 DPS
Charged Shot             |25-125
Sentry Turret            |3 dmg/tick
Teleporter

Zenyatta
Orb of Destruction       |45
Charged Orbs             |175 (35x5)
Orb of Discord           |N/A

Dva
Auto                     |24 (8x3)
Jet Booster              |25
Sidearm                  |14
Self-Destruct            |~100-1000

Reinhardt
Rocket Hammer            |75
Fire Strike              |100
Charge initial hit       |50
Charge impact            |300
Earthshatter             |100

Roadhog
Scrap Gun                |Up to 225
Mid Range Shot (Impact)  |50
Mid Range Shot (Spread)  |Up to 225
Chain Hook               |30
Whole Hog                |Theoretically 2500+

Winston
Tesla Cannon             |~3/tick
100 rounds               |294
Jump Pack                |15-50
Primal Rage              |40

Zarya
Particle Cannon          |~3/unit of ammo
Explosive Charge         |37
Graviton Surge           |22 (2x11)

Here is a link to a Reddit thread dicussing the weapon DPS, I'm not sure how accurate or up to date the information is. It links to this spreadsheet which seems to be a very comprehensive list including both regular weapon damage and damage vs armor.