If I start now, can I catch every Pokémon in Pokémon Go?

edit: the list is getting a bit out of date. I do not have time right now to update it, but a lot of previous legendaries are obtainable via the 7-day research reward, or coming back into legendary raids. Also, trading is now a thing, making it a lot easier to get eveerything you missed. The only ones you currently misseed are via special quests. These quests should have been picked up (but not completed) in a certain time period. Rewards for those were:

• Mew
• Celebi
• Spiritomb
• Meltan (but obtainable via a Mystery Box)

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There were multiple limited time Pokemon, mostly legendaries. It is currently not known if they will return (all of them or a select group). These Pokemon were:

1. (Shiny) Lugia
2. Articuno
3. Moltres
4. Zapdos
5. Raikou
6. Entei
7. Suicune
8. (Shiny) Ho-oh
9. Delibird
10. Groudon
11. Kyogre

Currently there is another legendary active, Latios/Latias (and shiny Ho-Oh), so be sure to catch that one while it is still possible. Also Mewtwo is available through Ex-raids at this moment in time.

The legendary birds (Articuno, Moltres, Zapdos) were twice catchable. First a week per bird, then about another month where all 3 birds were available at the same time. Now Zapdos is available by finishing a research quest on 7 individual days. Moltres was already available. Articuno will be available in June.

Another 'issue' might be the special hats for the Pikachu family. At specific moments in time they were catchable/hatchable with a different hat.

One other thing that might be annoying is that there are regional Pokemon. For example, Farfetch'd is limited to Asia only. However, there has been an event where it was catchable for 48 hours worldwide. You can still catch Farfetch'd in Asia, but not so soon in your hometown (if not located in Asia) though.

The regions of Seviper and Zangoose are switched right now. Catch the one that should not be in your location!

Posting an updated answer since the old one is outdated.

Kanto Pokedex. All Pokemon are obtainable.

Jotho Pokedex. All Pokemon are obtainable.

Hoenn Pokedex. Kecleon is the only unobtainable Pokemon.

Sinnoh Pokedex. The unobtainable Pokemon are:

• Rotom (all forms except for Wash are unobtainable)
• Phione and Manaphy
• Shaymin (both forms)
• Arceus (all forms)

Unova Pokedex. The unobtainable Pokemon are:

• Zorua + Zoroark

• Druddigon

• Larvesta + Volcarona

• Kyurem-Black and Kyurem-White (base form is available)

• Keldeo (both forms)

• Meloetta (both forms)

• Genesect Shock, Chill and Douse Drive forms (base and Burn Drive forms are available)

• Zen mode Darmanitan (Unovan and Galarian, base modes are available)

Kalos Pokedex. The following Pokemon and their evolutions are available:

• Chespin

• Fennekin

• Froakie

• Bunnelby

• Fletchinder

• Litleo

• Pancham

• Espurr

• Spiritzee

• Swirlex

• Binacle

• Skrelp

• Clauncher

• Sylveon

• Goomy

• Noibat

• Xerneas

• Yveltal

Alolan Pokedex. No Pokemon are obtainable. However, all Alolan variants of Kanto Pokemon are available.

Galarian Pokedex. Obstagoon, Persekker, Sirfetch'd, Runerigus, and Mr Rime are obtainable, as well as all Galarian forms except Articuno, Zapdos, Moltres, Corsola and Slowking.

Unknown Pokedex. All Pokemon are obtainable (Meltan and Melmetal)

Many of the obtainable Pokemon can't currently be caught, for example most legendaries. If starting now, you'll need to trade with a player to obtain these Pokemon. For Pokemon that cannot be traded (Mythical Pokemon other than Meltan and Melmetal), this renders Mythicals that aren't currently available to be unavailable by any means until they became available again. Mew, Celebi, Jirachi, and Victini are available through special quests that do not have a time limit; hence they can still be obtained.

The unobtainable Pokemon that have previously been released are:

• Deoxys (all formes)
• Darkrai
• Genesect