The following Pokémon have new locations in Pokémon Emerald, these Pokémon could previously not be obtained without trading:

STARTERS
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CHARMANDER - Fiery Path
WARTORTLE - Victory Road (Surf, B2F)	
IVYSAUR - Route 119
QUILAVA - Route 112
CROCONAW - Route 124 (Fishing Rod)
CHIKORITA - Safari Zone
COMBUSKEN - Magma Hideout (3F 3R)
SWAMPERT - Meteor Falls (B1F 1R, Fishing Rod) 
TREECKO - Petalburg Woods  

KANTO POKÉMON 
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CATERPIE - Petalburg Woods  
WEEDLE - Route 101
SPEAROW - Route 104
PIDGEY - Route 110
RATTATA - Route 101
WEEPINBELL - Safari Zone
EXEGGCUTE - Route 120
VENONAT - Safari Zone
PARASECT - Safari Zone
TANGELA - Safari Zone
ONIX - Magma Hideout
GROWLITHE - Magma Hideout
PONYTA - Jagged Pass
EEVEE - Route 103
SPEAROW - Route 103
DITTO - Scorched Slab
LAPRAS - Meteor Falls (1F 1R, Surf)
NIDORAN Male - Route 111
NIDORAN Female - Route 123
DRATINI - Safari Zone (Fishing Rod)
HITMONCHAN - Mt. Pyre (Exterior)
HITMONLEE - Jagged Pass
CLEFAIRY - Meteor Falls (B1F 2R, Route 114)
ARBOK - Mt. Pyre (Exterior)
POLIWHIRL - Safari Zone (Surf)
SLOWPOKE - Route 134 (Surf)
DIGLETT - Granite Cave
PERSIAN - Route 115
PRIMEAPE - Safari Zone 
TAUROS - Safari Zone
MR. MIME - Route 121
FARFETCH'D - Route 119
KINGLER - Pacifidlog Town (Super Rod)
CLOYSTER - Shoal Cave (Ice Room)
LICKITUNG - Safari Zone
CUBONE - Route 111
KANGASKHAN - Route 113
CHANSEY - Safari Zone Expansion (Area 6)
KABUTO - Underwater
OMANYTE - Underwater
AERODACTYL - Mt. Pyre (Exterior)
SNORLAX - Route 115

JOHTO POKÉMON
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SENTRET - Route 103
MISDREAVUS - Safari Zone Expansion (Area 5)
MURKROW - Safari Zone Expansion (Area 6)
SKIPLOOM - Route 115
SUNKERN - Route 117
ELEKID - New Mauville
MAGBY - Jagged Pass
PILOWSWINE - Shoal Cave (Ice Room)
SMOOCHUM - Shoal Cave (Ice Room)
SNEASEL - Shoal Cave (Ice Room)
TOGEPI - Route 117
ESPEON - Mt. Chimney (Exterior)
UMBREON - Jagged Pass
DUNSPARCE - Shoal Cave (Entrance Room)
UNOWN - Cave of Origin
PINECO - Petalburg Woods
QWILFISH - Dewford Town (Super Rod)
SHUCKLE - Magma Hideout
DELIBIRD - Shoal Cave (Ice Room)
MANTINE - Route 103 (Surf)
PORYGON2 - New Mauville
LARVITAR - Route 121
KINGDRA - Safari Zone Expansion (Area 5, Super Rod)

HOENN POKÉMON
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SURSKIT - Routes 102, 111, 114, 117, and 120
MEDITITE- Mt. Pyre, Victory Road
MEDICHAM - Victory Road
ROSELIA - Route 117
ZANGOOSE - Route 114
LUNATONE - Meteor Falls
MAWILE - Granite Cave

TRADE EVOLUTIONS
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SCIZOR - Safari Zone Expansion (Area 6)
STEELIX - Cave of Origin
GOLEM - Magma Hideout
ALAKAZAM - Mt. Pyre (Exterior)
GENGAR - Mt. Pyre (Interior)
POLITOED - Seafloor Cavern (Room 6)
SLOWKING - Meteor Falls (B1F 1R)
MACHAMP - Victory Road

LEGENDARY POKÉMON 
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You do not need the event tickets to get to these legendaries anyomore, there is a new area in the Cave of Origin that has warps to get to the secret islands. 

LATIOS/LATIAS - Southern Island
DEOXYS - Birth Island
HO-OH/LUGIA - Navel Rock
MEW - Faraway Island

UNOBTAINABLE POKÉMON
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You cannot catch the following Pokémon:

JIRACHI
CELEBI
ARTICUNO
ZAPDOS
MOLTRES
MEWTWO
ENTEI
SUICUNE
RAIKOU

You can transfer Mewtwo, Entei, Suicune, Raikou, Zapdos, Articuno and Moltres from a save of Fire Red or Leaf Green.