NOTE: I am using the Gen 6+ type chart in which Electric-types cannot be Paralysed.
ANOTHER NOTE: The ability that gives the Pokemon immunity to :status condition: is listed in (parenthesis) after the stated immunity.
ANOTHER ANOTHER NOTE: I am not including the ability Flash Fire, as those Pokemon can still be Burned by Tri Attack, or the ability Hydration, as you can technically still give these Pokemon status conditions but they are healed at the end of the turn of it is Raining.
Gen 1
- Magby/Magmar/Magmortar: Immune to Burns and Sleep (Vital Spirit)
- Elekid/Electabuzz/Electivire: Immune to Paralysis and Sleep (Vital Spirit)
- Galarian Slowbro/Slowking: Immune to Poison and Confusion (Own Tempo)
- Mr. Rime: Immune to Freezing and Sleep (Vital Spirit)
- Alolan Sandshrew/Sandslash: Immune to Freezing and Poison
- Magnemite/Magneton/Magnezone: Immune to Paralysis and Poison
Gen 2
- Spinarak/Ariados: Immune to Sleep (Insomnia) and Poison
Slugma/Magcargo: Immune to Burns and Freezing (Magma Armor)
Gen 3
- Numel: Immune to Burns and Confusion (Own Tempo)
- Camerupt: Immune to Burns and Freezing (Magma Armor)
- Roselia/Budew: Immune to Poison by typing and Freezing/Burns/Paralysis/Sleep/Poison if they have Leaf Guard and it is Sunny
Gen 4
- Heatran: Immune to Burns and Poison
- Heat Rotom: Immune to Paralysis and Burns
- Frost Rotom: Immune to Freezing and Paralysis
Gen 7
- Togedemaru: Immune to Poison and Paralysis
- Salandit/Salazzle: Immune to Burns and Poison
- Komala: Immune to Sleep/Poison/Paralysis/Burns/Freezing (Comatose)
Gen 8
- Arctozolt: Immune to Freezing and Paralysis
- Toxtricity: Immune to Poison and Paralysis
- Galarian Darmanitan Zen Mode: Immune to Burns and Freezing
I don't think any Pokemon are immune to Curse/Nightmare.
Please comment if I missed something.