I've been looking up rare Pokemon today. According to Serebii.net's lists, the only Pokemon which cannot be caught at all in Generation IV are Mew, Celebi, Jirachi, and Deoxys.
Several others can technically be caught, but require some event: Regigigas, Regirock, Regice, Registeel, Phione, Manaphy, Darkrai, Shaymin, and Arceus.
Darkrai and Shaymin were unlocked by Wi-Fi event, but if you missed them, you're out of luck. Mew and Jirachi were distributed over Wi-Fi, but only in Japan.
Manaphy, Phione, Mew, Darkrai and Shaymin are available via various Pokemon spinoff games for DS or Wii. My Pokemon Ranch gives Mew and Phione (requires Diamond/Pearl), Darkrai and Shaymin are available via two separate Pokemon Ranger games, and Manaphy (and Phione by breeding) are available via any of three Pokemon Ranger games.
Regirock, Regice, and Registeel are found in Ruby/Sapphire/Emerald. These unlock Regigigas in DPPt. Should you have acquired Regigigas by event, it unlocks the other three golems in DPPt.
Jirachi requires either Ruby/Sapphire, and either Pokemon Channel (EU/AUS) or Pokemon Colosseum (US, with bonus pre-order disc) for Gamecube.
Arceus and Deoxys have only been released by event. If you missed them, tough.
Celebi requires Ruby/Sapphire/Emerald, and Pokemon Colosseum (JP, with bonus disc) for Gamecube. Unless Colosseum can trade to foreign games, the trade requires a Japanese copy of Ruby/Sapphire and a Japanese Generation IV game. Celebi has been released only once in the US, at a physical event in 2006.