The only ones I can think of are Toxitricity, galarian zen mode darmanitan, and salandit/salazzle. Just to be clear, I mean the elemental status conditions, burn, frozen, paralyzed, or poisoned, not confused, as I don't think any typing resists confusion, although if there is an ability that makes the Pokémon immune to confusion, list the Pokemon that have that ability, as I wouldn't know.
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
Gen 2
Gen 3
Gen 4
Gen 7
Gen 8
I don't think any Pokemon are immune to Curse/Nightmare.
Please comment if I missed something.
Technically every single Pokemon is immune to a few Sleep moves and Stun Spore if they hold Safety Goggles.
Will try to complete later
Update for Gen 9
Garganacl: Immune to all Status conditions via Purifying Salts.
Scovillain: Immune to burn via Fire Type and Sleep via Insomnia.
Tinkatink/Tinkatuff/Tinkaton: Immune to poison via Steel type and confusion via Own Tempo.
Frigibax/Artibax/Baxcalibur: Immune to freezing via Ice type and Burn via Thermal Exchange.
Hisuian Lilligant: Immune to all Status conditions while in harsh sunlight via Leaf Guard.