I've done this before with Platinum, and no doubt HGSS will bring its fair share of tutors and level-up additions. Will we go to the Twilight Zone once more, with a previously overlooked Pokémon catapulting itself to the top of the charts?
Anyway, you know the drill now: I will only add moves that are relevant to the Pokémon, so no moves that are obsoleted by another one (for example, Heat Wave on all these Fire-types in Platinum), no attacking moves on Pokémon that clearly specialize in the opposing category (example from Platinum: Heat Wave wasn't listed for Staraptor), no ultra-weak attack moves (another Platinum example: TWISTER), and no NFEs except for the competitively relevant ones.
When a Pokémon is in blue, it means it hasn't been fully checked, when it's red, it means it's confirmed to get nothing new, and when it's black, it has been fully checked and all its moves are listed.
#003 - VENUSAUR - Block, Power Whip
#006 - CHARIZARD - Tailwind
#009 - BLASTOISE - Water Spout
#012 - BUTTERFREE
#015 - BEEDRILL
#018 - PIDGEOT
#020 - RATICATE
#022 - FEAROW
#024 - ARBOK - Switcheroo
#025 - PIKACHU - Flail, Fly
#026 - RAICHU - Flail, Fly
#028 - SANDSLASH - Super Fang
#031 - NIDOQUEEN - Super Fang
#034 - NIDOKING - Head Smash, Super Fang
#036 - CLEFABLE - Aromatherapy, Heal Bell, Magic Coat
#038 - NINETALES - Pain Split
#040 - WIGGLYTUFF - Heal Bell, Magic Coat, Pain Split
#045 - VILEPLUME - Teeter Dance, Worry Seed
#047 - PARASECT - Agility, Worry Seed
#049 - VENOMOTH
#051 - DUGTRIO - Reversal
#053 - PERSIAN
#055 - GOLDUCK - Encore, Low Kick, Worry Seed
#057 - PRIMEAPE - Encore
#059 - ARCANINE - Morning Sun
#062 - POLIWRATH - Encore
#065 - ALAKAZAM - Gravity
#068 - MACHAMP
#071 - VICTREEBEL - Weather Ball
#073 - TENTACRUEL - Magic Coat
#076 - GOLEM - Curse
#078 - RAPIDASH - Morning Sun
#080 - SLOWBRO - Magic Coat
#083 - FARFETCH'D - Leaf Blade
#085 - DODRIO
#087 - DEWGONG - Stockpile
#089 - MUK - Pain Split
#091 - CLOYSTER - Rock Blast
#094 - GENGAR - Pain Split
#097 - HYPNO - Low Kick, Magic Coat
#099 - KINGLER - Agility
#101 - ELECTRODE
#103 - EXEGGUTOR - Low Kick, Gravity
#105 - MAROWAK - Low Kick
#106 - HITMONLEE - Low Kick
#107 - HITMONCHAN - Low Kick
#110 - WEEZING
#115 - KANGASKHAN - Low Kick
#119 - SEAKING
#121 - STARMIE - Gravity, Magic Coat, Pain Split
#122 - MR. MIME - Nasty Plot
#123 - SCYTHER - Bug Bite
#124 - JYNX - Heal Bell, Nasty Plot
#127 - PINSIR
#128 - TAUROS
#130 - GYARADOS
#131 - LAPRAS - Block
#132 - DITTO
#134 - VAPOREON - Heal Bell
#135 - JOLTEON - Heal Bell
#136 - FLAREON - Heal Bell
#139 - OMASTAR
#141 - KABUTOPS - Low Kick
#142 - AERODACTYL
#143 - SNORLAX - Counter
#144 - ARTICUNO
#145 - ZAPDOS
#146 - MOLTRES
#149 - DRAGONITE - Extremespeed
#150 - MEWTWO - Gravity, Low Kick
#151 - MEW - Block, Gravity, Low Kick, Pain Split, Super Fang, Worry Seed
#154 - MEGANIUM - Magic Coat, Worry Seed
#157 - TYPHLOSION - Low Kick, Extrasensory
#160 - FERALIGATR - Aqua Jet, Low Kick
#162 - FURRET - Super Fang
#164 - NOCTOWL - Magic Coat
#166 - LEDIAN
#168 - ARIADOS
#169 - CROBAT - Super Fang, Tailwind
#171 - LANTURN - Heal Bell
#178 - XATU - Magic Coat, Pain Split
#181 - AMPHAROS
#182 - BELLOSSOM - Teeter Dance, Worry Seed
#184 - AZUMARILL
#185 - SUDOWOODO
#186 - POLITOED - Encore
#189 - JUMPLUFF
#192 - SUNFLORA - Earth Power
#195 - QUAGSIRE - Recover
#196 - ESPEON - Heal Bell, Magic Coat
#197 - UMBREON - Heal Bell
#199 - SLOWKING - Magic Coat
#201 - UNOWN
#202 - WOBBUFFET
#203 - GIRAFARIG - Gravity
#205 - FORRETRESS - Block, Gravity, Pain Split, Power Trick
#206 - DUNSPARCE - Agility, Pain Split
#208 - STEELIX
#210 - GRANBULL - Low Kick, Super Fang
#211 - QWILFISH - Aqua Jet, Pain Split
#212 - SCIZOR - Bug Bite
#213 - SHUCKLE
#214 - HERACROSS - Low Kick
#217 - URSARING - Belly Drum, Low Kick
#219 - MAGCARGO - Pain Split
#222 - CORSOLA - Curse, Magic Coat
#224 - OCTILLERY - Water Spout
#225 - DELIBIRD - Fake Out
#226 - MANTINE
#227 - SKARMORY
#229 - HOUNDOOM - Super Fang
#230 - KINGDRA
#232 - DONPHAN - Block, Head Smash
#233 - PORYGON2 - Gravity, Pain Split
#234 - STANTLER - Gravity, Megahorn
#235 - SMEARGLE
#237 - HITMONTOP - Low Kick
#241 - MILTANK - Block
#242 - BLISSEY - Block
#243 - RAIKOU
#244 - ENTEI
#245 - SUICUNE
#248 - TYRANITAR - Block, Low Kick
#249 - LUGIA - Dragon Rush, Tailwind, Weather Ball
#250 - HO-OH - Brave Bird, Tailwind, Weather Ball
#251 - CELEBI - Magic Coat, Worry Seed
#254 - SCEPTILE - Low Kick
#257 - BLAZIKEN - Low Kick
#260 - SWAMPERT - Low Kick, Yawn
#262 - MIGHTYENA - Super Fang
#264 - LINOONE - Super Fang
#267 - BEAUTIFLY - Tailwind
#269 - DUSTOX - Tailwind
#272 - LUDICOLO - Counter
#275 - SHIFTRY - Low Kick, Tailwind
#277 - SWELLOW
#279 - PELIPPER
#282 - GARDEVOIR - Encore, Heal Bell, Pain Split
#284 - MASQUERAIN
#286 - BRELOOM
#288 - VIGOROTH - Low Kick
#289 - SLAKING - Block, Low Kick
#291 - NINJASK
#292 - SHEDINJA
#295 - EXPLOUD - Low Kick, Hammer Arm
#297 - HARIYAMA - Low Kick
#301 - DELCATTY
#302 - SABLEYE - Gravity, Low Kick, Pain Split
#303 - MAWILE - Pain Split, Super Fang
#306 - AGGRON - Block, Head Smash, Low Kick
#308 - MEDICHAM - Gravity, Low Kick, Magic Coat, Pain Split
#310 - MANECTRIC - Switcheroo
#311 - PLUSLE - Discharge
#312 - MINUN - Discharge
#313 - VOLBEAT - Tailwind
#314 - ILLUMISE - Tailwind
#317 - SWALOT - Block
#319 - SHARPEDO - Super Fang
#321 - WAILORD - Aqua Ring, Block
#323 - CAMERUPT - Stockpile
#324 - TORKOAL
#326 - GRUMPIG - Heal Bell
#327 - SPINDA - Low Kick
#328 - TRAPINCH
#330 - FLYGON - Tailwind
#332 - CACTURNE - Nasty Plot, Worry Seed
#334 - ALTARIA
#335 - ZANGOOSE - Low Kick
#336 - SEVIPER - Switcheroo
#337 - LUNATONE - Gravity, Magic Coat, Pain Split
#338 - SOLROCK - Gravity, Magic Coat, Pain Split
#340 - WHISCASH - Dragon Dance
#342 - CRAWDAUNT - Dragon Dance
#344 - CLAYDOL - Gravity, Magic Coat
#346 - CRADILY - Block, Curse, Pain Split, Worry Seed
#348 - ARMALDO - Block, Curse, Low Kick
#350 - MILOTIC - Magic Coat
#351 - CASTFORM - Tailwind
#352 - KECLEON - Low Kick, Recover
#354 - BANETTE - Pain Split
#357 - TROPIUS - Dragon Dance, Tailwind, Worry Seed
#358 - CHIMECHO - Gravity
#359 - ABSOL - Megahorn
#362 - GLALIE - Super Fang, Weather Ball
#365 - WALREIN - Aqua Ring, Block, Super Fang
#366 - CLAMPERL
#367 - HUNTAIL - Super Fang
#368 - GOREBYSS
#369 - RELICANTH
#370 - LUVDISC - Aqua Jet
#373 - SALAMENCE - Tailwind
#376 - METAGROSS - Block, Gravity
#377 - REGIROCK - Block, Gravity
#378 - REGICE - Block, Gravity
#379 - REGISTEEL - Block, Gravity
#380 - LATIAS - Magic Coat, Tailwind
#381 - LATIOS - Magic Coat, Tailwind
#382 - KYOGRE - Aqua Ring, Block
#383 - GROUDON - Block, Hammer Arm
#384 - RAYQUAZA - Air Slash
#385 - JIRACHI - Headbutt, Magic Coat
#386 - DEOXYS - Gravity, Low Kick
#389 - TORTERRA - Block, Stockpile
#392 - INFERNAPE - Low Kick
#395 - EMPOLEON
#398 - STARAPTOR
#400 - BIBAREL
#402 - KRICKETUNE - Taunt
#405 - LUXRAY - Night Slash
#407 - ROSERADE
#409 - RAMPARDOS - Curse, Pain Split
#411 - BASTIODON - Counter
#413P - WORMADAM-P - Worry Seed
#413G - WORMADAM-G
#413S - WORMADAM-S
#414 - MOTHIM - Tailwind
#416 - VESPIQUEN - Tailwind
#417 - PACHIRISU
#419 - FLOATZEL - Low Kick
#421 - CHERRIM - Weather Ball
#423 - GASTRODON - Block, Pain Split
#424 - AMBIPOM - Low Kick
#426 - DRIFBLIM - Magic Coat, Pain Split, Tailwind, Weather Ball
#428 - LOPUNNY - Flail, Heal Bell
#429 - MISMAGIUS - Heal Bell, Nasty Plot
#430 - HONCHKROW - Brave Bird, Tailwind
#432 - PURUGLY - Flail, Super Fang
#435 - SKUNTANK - Haze
#437 - BRONZONG - Gravity
#441 - CHATOT
#442 - SPIRITOMB
#445 - GARCHOMP
#448 - LUCARIO
#450 - HIPPOWDON - Revenge
#452 - DRAPION
#454 - TOXICROAK - Counter, Low Kick, Super Fang
#455 - CARNIVINE
#457 - LUMINEON
#460 - ABOMASNOW - Block, Worry Seed
#461 - WEAVILE - Low Kick
#462 - MAGNEZONE - Gravity, Magic Coat
#463 - LICKILICKY - Block
#464 - RHYPERIOR - Block
#465 - TANGROWTH - Pain Split, Worry Seed
#466 - ELECTIVIRE
#467 - MAGMORTAR - Belly Drum, Low Kick
#468 - TOGEKISS - Heal Bell, Magic Coat, Tailwind
#469 - YANMEGA - Tailwind
#470 - LEAFEON - Heal Bell, Worry Seed
#471 - GLACEON - Heal Bell
#472 - GLISCOR
#473 - MAMOSWINE - Block
#474 - PORYGON-Z - Gravity, Pain Split
#475 - GALLADE - Encore, Low Kick, Pain Split
#476 - PROBOPASS - Head Smash, Pain Split
#477 - DUSKNOIR
#478 - FROSLASS - Pain Split, Weather Ball
#479 - ROTOM - Pain Split
#480 - UXIE - Heal Bell, Magic Coat
#481 - MESPRIT - Magic Coat
#482 - AZELF
#483 - DIALGA - Gravity, Metal Burst, Power Gem
#484 - PALKIA - Gravity, Hydro Pump, Power Gem
#485 - HEATRAN
#486 - REGIGIGAS - Block, Gravity
#487 - GIRATINA - Destiny Bond, Gravity, Magic Coat, Pain Split, Shadow Sneak, Tailwind
#488 - CRESSELIA - Magic Coat
#490 - MANAPHY - Heal Bell
#491 - DARKRAI
#492 - SHAYMIN - Tailwind, Worry Seed
#493 - ARCEUS - Magic Coat, Tailwind
NOTE: Giratina and Shaymin can only obtain Tailwind (and Magic Coat in Giratina's case) in their Origin and Sky forms, but can pass it to their regular forms by changing back