There is one Pokémon line in the series that lacks any kind of weaknesses, thanks to its unique ability and type combination. The type system in the Pokémon video games is a major component of combat and entire teams are built with type composition in mind, as players want to ensure that they deal and resist as much damage as possible. The Pokémon weakness and resistance system, coupled with the ability to create a team with a mixture of dual-types, means that there is a lot of depth to the competitive battling scene, even before factoring in things like abilities and moves.
A Pokémon's type determines the amount of damage it will take from types used by different attacks. Pokémon can be weak to a type (takes double damage), resistant to damage (takes half damage), or immune to a type (takes no damage). A Pokémon with multiple types can potentially take quadruple damage from an attack, such as the Rock/Ground-type Onix when hit by a Grass-type or Water-type move. It took a while for the type system to be balanced out, as people who suffered through the reign of overpowered Psychic-type Pokémon in Red & Blue can attest, and it's something that is still occasionally tweaked by Game Freak.
There was a time when several Pokémon lacked weaknesses, due to their type combination. From Gen II-V, a Pokémon with the Dark/Ghost-type combination had no weaknesses and would be totally immune to Fighting, Psychic, and Normal-type attacks. The first Pokémon to have this mixture of typing was Sableye from Pokémon Ruby and Sapphire. The second Pokémon to have this type of combination was Spiritomb from Pokémon Diamond and Pearl. This changed in Pokémon X & Y, when the Fairy-type was introduced, as this gave both of them a new weakness to contend with. This means that Sableye's weakness is Fairy-type moves and Spiritomb's weakness is Fairy-type moves. There is now only a single Pokémon line left with no weaknesses, thanks to a combination of factors.
Pokémon's Mighty Floating Electric-Type Eelektross Is (Almost) Invincible
The Eelektross line (Tynamo, Eelektrik, and Eelektross) all lack any weaknesses. The reason for this is that they are pure Electric-type Pokémon that can only possess the Levitate ability. Levitate makes the user immune to Ground-type moves, which is the primary opponent to Electric-type users. Ground-type Pokémon are completely immune to Electric-type moves, which is why the writers of the Pokémon anime had to jump through hoops to let Pikachu beat Brock's Onix. Electric-type Pokémon are normally weak to Ground-type moves, but Eelektross and its previous forms are the exceptions. It's possible to negate Levitate with the aid of certain moves, like Smack Down, or if the enemy Pokémon has a counter ability, like Neutralizing Gas, so there are ways to give Eeleltross a weakness to Ground-type moves.
This doesn't mean Eelektross is some powerhouse in competitive battles. Eelektross only has three resistances (Electric, Steel, and Flying), so it's not considered to be a defensive wall. It's a powerful attacker, but its low speed and defensive stats make it easy pickings for other Pokémon. Eelektross was one of the Pokémon that didn't survive the jump into Pokémon Sword & Shield, so it's unclear how it would fit into the current competitive battling scene, but there's a good chance it will return when Pokémon Black & White receive remakes, as they're next in line after the Sinnoh games.