What Attacks Can D.Va's Shield Block (or Not Block)?

Blocking Ultimates

According to Furious Paul's D.va In-depth Strategy Guide, Defense Matrix will block most ultimates in the game, including

Roadhog's Whole Hog
Soldier 76's Tactical Visor
McCree's Deadeye
Reaper's Death Blossom
Pharah's Barrage
Bastion's Tank Form

Defense Matrix will also block the following:

Zarya's Graviton Surge (before it detonates)

According to PSA - DVA Shield Completely Nullifies Hanzos Ult if Directly Hit, Defense Matrix will block Hanzo's ultimate both when it's an arrow (before it summons dragons), as well as after the arrow summons the dragons:

The PSA is that unlike Genji's deflection which deflects the initial arrow but doesn't stop Hanzo's dragons appearing, the projectile-blocking shield actually stops the entire ult.

However, I haven't confirmed this myself, so I don't know how reliable that comment is.

Blocking Other Abilities and Attacks

Also according to Paul's D.Va guide, Defense Matrix will not work on

All melee attacks.

All channeled weapons, including:

Mei's Endothermic Blaster (short range freeze gun),

Winston's Tesla Cannon,

Symmetra's Photon Projector Beam,

Zarya's Particle Cannon beam.

Lucio's Blast of Sound (alternate fire).

Zenyatta's Orb of Discord.

Symmetra's Sentry Turrets.

Roadhog's Chain Hook.

Defense Matrix will also block the following:

Reinhardt's Fire Strike
McCree's Flashbang

The list of projectiles D.Va can block is nearly identical to the list of projectiles Genji can reflect.

The main difference is that, unlike Genji, D.Va cannot negate damage from Melee and physical attacks, such as Winston's Primal Rage or Reinhardt's Rocket Hammer. I also have yet to test whether D.Va can block Soldier 76's Biotic Field.

D.Va can block

Ana's Biotic Rifle (scoped & unscoped), Sleep Dart, and Biotic Grenade
Bastion's Recon fire, Sentry fire, and Tank projectiles
D.Va's Fusion Cannons and Light Gun Pistol
Genji's Shuriken and Deflected projectiles
Hanzo's Storm Bow, Sonic Arrow, Scatter Arrow, and Dragonstrike (Arrow)¹
Junkrat's Frag Launcher Grenades, Concussion Mine², and Total Mayhem Grenades
Lucio's Sonic Amplifier (Primary)
McCree's Revolver, Flashbang, and Deadeye
Mei's Icicle and Blizzard²
Mercy's Caduceus Blaster
Orisa's Fusion Driver and Halt
Pharah's Rocket Launcher, Concussive Blast, and Rocket Barrage
Reaper's Shotgun and Death Blossom (Source)
Reinhardt's Fire Strike
Roadhog's Scrap Gun, Chain Hook and Whole Hog
Soldier 76's Pulse Rifle, Helix Rockets, and Tactical Visor
Sombra's Machine Pistol
Symmetra's Energy Ball
Torbjörn's Rivet Gun and Turret bullets
Tracer's Pulse Pistols and Pulse Bomb
Widowmaker's Sniper, Assault Rifle, and Venom Mine²
Zarya's Particle Cannon projectile (secondary fire) and Graviton Surge³
Zenyatta's Orb of Destruction and Orb Volley

D.Va can not block

Ana's Nano Boost
D.Va's Boosters, Call Mech, and Self-Destruct
Genji's Swift Strike and Dragonblade
Hanzo's Dragonstrike (Dragons)¹
Junkrat's Steel Trap and RIP-Tire
Lucio's Sonic Amplifier (Alternate) and Sound Barrier
Mei's Endothermic Blaster frost and Ice Wall
Orisa's Protective Barrier and Supercharger
Reinhardt's Rocket Hammer, Charge, and Earthshatter
Sombra's Hack, Translocator, and EMP
Symmetra's Photon Projector beam, Photon Barrier, and Sentry Turrets
Torbjörn's Hammer and Armor Packs
Widowmaker's Grappling Hook
Winston's Tesla Cannon, Jump Pack, Barrier Projector, and Primal Rage
Zarya's Particle Cannon beam (primary fire)
Zenyatta's Orb of Harmony and Orb of Discord
All character's standard Melee attacks

Unknown

Soldier 76's Biotic Field

Sources

What Attacks Can D.Va's Shield Block (or Not Block)?
Does D.Va's Defense Matrix completely nullify Reaper's ult?
Overwatch Wikia - Defense Matrix

Notes

¹Hanzo's ultimate is fired as a blockable arrow before transforming into unblockable dragons.
²Only blockable in midair before it hits the ground.
³Graviton Surge only blockable in midair before it detonates.