Okay, I'm going to do my best to list Pokemon that are exclusive to the Dream World, like Bolt said, and also Pokemon that are useful competitively, like I said.
Dream World Exclusives (i.e., Dream World abilities cannot be obtained in-game. Does not include Pokemon that have been released as past events, since you can't get those in the Dream World anymore)
Kanto families
Pidgey
Rattata
Spearow
Ekans
Sandshrew
Igglybuff (also available on Dream Radar)
Zubat
Oddish
Paras
Diglett
Growlithe
Abra
Machop
Bellsprout
Tentacool
Geodude
Ponyta
Slowpoke (also available on Dream Radar)
Magnemite
Farfetch'd
Doduo
Seel
Shellder
Onix
Drowzee
Voltorb
Exeggcute
Cubone
Tyrogue (since Tyrogue is always male, if you want a DW Hitmonlee, Hitmonchan, or Hitmontop, you will need three Tyrogues)
Lickitung
Chansey
Tangela
Kangaskhan
Horsea
Goldeen/Seaking
Staryu (also available on Dream Radar)
Mr. Mime
Scyther
Smoochum (also available on Dream Radar)
Elekid
Magby
Tauros
Magikarp
Lapras
Eevee (if you want a female. A male is a gift in Castelia City)
Omanyte
Kabuto
Aerodactyl
Johto families
Sentret
Hoothoot (also available on Dream Radar)
Ledyba
Spinarak
Chinchou
Natu
Mareep
Sudowoodo
Hoppip
Aipom
Sunkern
Yanma
Wooper
Girafarig
Pineco
Qwilfish
Shuckle (also available on Dream Radar)
Slugma
Swinub
Remoraid
Delibird
Mantine
Skarmory
Houndour
Stantler
Smeargle
Miltank
Larvitar
Hoenn families
Poochyena
Zigzagoon
Wurmple
Seedot
Taillow
Surskit
Nincada
Whismur
Skitty
Aron
Volbeat
Illumise
Roselia
Gulpin
Carvanha
Wailmer
Numel
Torkoal
Spoink
Trapinch
Cacnea
Barboach
Corphish
Lileep
Anorith
Feebas
Shuppet
Tropius
Snorunt
Clamperl
Relicanth
Luvdisc
Sinnoh Families
Staravia
Kricketot
Shinx
Burmy
Buizel
Drifloon (also available on Dream Radar)
Buneary
Gible
Hippopotas
Croagunk
Finneon
Snover
Unova families
Pidove
Boldore
Woobat
Drilbur
Audino
Gurdurr
Tympole
Throh
Sawk
Scolipede
Cottonee
Petilil
Basculin
Krookodile
Maractus
Crustle
Scraggy
Sigilyph (also available on Dream Radar)
Tirtouga
Duosion
Ducklett
Vanillish
Emolga
Karrablast
Alomomola
Galvantula
Klang
Elgyem
Axew
Shelmet
Stunfisk
Druddigon
Golett
Pawniard
Heatmor
Durant
If you are playing as a BOY, you will also need to get these Pokemon:
Mankey
Cranidos
Sableye
Phanpy
If you're playing as a GIRL, you will also need to get these Pokemon:
Meowth
Shieldon
Teddiursa
Mawile
Pokemon that are competitively useful (in my opinion. Others will probably add or take away from this list):
Female:
Vulpix
Poliwag
Abra
Eevee (for Magic Bounce Espeon and Hydration Vaporeon)
Gligar
Bagon
Dratini
Sableye
Gible
Shellder
Magikarp
Tentacool
Male: (many of these can be taught the moves at Move Tutors for Shards)
Stealth Rocks Larvitar
Roost Skarmory
Stealth Rocks Aeordactyl
Bounce Magikarp
Outrage Bagon
anything that learns Stealth Rocks, Roost, Sucker Punch, Dark Pulse, Drain Punch, Thunder/Fire/Ice Punch, Baton Pass, Nasty Plot, Fake Out, or Outrage that you think might be useful for breeding purposes.
Nice list, but I'd like to point out that some of the Pokemon available in Hidden Grottoes, the Dream Radar, and the Yancy/Curtis trades are not available in BW2's Dream World. And since alessandrae didn't specify whether or not she has BW1, it's worth pointing out which ones can't be obtained in BW2. These are the ones that are not available in BW2's Dream World (if you have BW1, you can get it in those games' DW, but otherwise you need to obtain it through the method mentioned):
Butterfree (Hidden Grotto in Pinwheel Forest)
Nidoran (Hidden Grotto on Rt. 2)
Clefairy (Hidden Grotto in Giant Chasm)
Igglybuff (Dream Radar)
Venonat (Hidden Grotto on Rt. 3)
Meowth (Trade with Yancy)
Mankey (Trade with Curtis)
Slowpoke (Dream Radar)
Grimer (Hidden Grotto on Rt. 9)
Krabby (Hidden Grotto on Rt. 18)
Rhyhorn (Trade with Yancy or Curtis)
Staryu (Dream Radar)
Smoochum (Dream Radar)
Hoothoot (Dream Radar)
Wobbuffet (Trade with Yancy or Curtis)
Dunsparce (Hidden Grotto in Flocessy Ranch or Rt. 6)
Shuckle (Dream Radar)
Teddiursa (Trade with Yancy)
Corsola (Hidden Grotto on Rt. 18)
Phanpy (Trade with Curtis)
Lotad (Hidden Grotto on Rt. 3)
Wingull (Hidden Grotto on Rt. 22)
Ralts (Dream Radar or Trade with Yancy or Curtis)
Makuhita (Hidden Grotto in Pinwheel Forest)
Nosepass (Hidden Grotto on Rt. 6)
Sableye (Trade with Curtis)
Mawile (Trade with Yancy)
Meditite (Hidden Grotto in Pinwheel Forest)
Electrike (Hidden Grotto on Rt. 3)
Spinda (Trade with Yancy or Curtis)
Swablu (Hidden Grotto in Abundant Shrine or Dream Radar)
Zangoose (Hidden Grotto on Rt. 7 and Rt. 23)
Seviper (Hidden Grotto on Rt. 7 and Rt. 23)
Spheal (Hidden Grotto on Rt. 13)
Beldum (Hidden Grotto in Giant Chasm or Dream Radar)
Cranidos (Trade with Curtis)
Shieldon (Trade with Yancy)
Combee (Hidden Grotto in Lostlorn Forest)
Pachirisu (Hidden Grotto on Rt. 3)
Shellos (Yancy gives you West Sea, Curtis gives you East Sea)
Drifloon (Hidden Grotto on Rt. 13 or Dream Radar)
Bronzor (Dream Radar)
Chatot (Hidden Grotto on Rt. 18)
Spiritomb (Trade with Yancy or Curtis)
Riolu (Dream Radar)
Skorupi (Hidden Grotto on Rt. 13)
You'll definitely need to do some trading to obtain all of them if you don't have BW1, at the very least you'll need to trade for Beedrill (which can only be obtained in BW1's Dream World and one of the Pinwheel Forest Hidden Grottoes in Black 2), Darmanitan (only catchable in BW1's post game and not available in any way in BW2) and either Curtis' Pokemon if you're playing as the male character or Yancy's Pokemon if you're playing as the female character.
I'm not going to bother debating which ones are competitively useful since my knowledge of competitive battling is somewhat limited, so I'm just going to leave your suggestions alone.