Usually defined by specialization in throw and grappling based attacks, grapplers (also called throw characters) are a staple of the fighting game genre with a representative in virtually every major fighting franchise.
Zangief, the wrestling giant from the Street Fighter series, is an iconic example dating back to the early nineties with many common attributes including relatively slow mobility, a large build and a focus on using multiple types of grabs to do the most damage.
Grapplers have a tendency to have command grabs, which tend to have additional properties and utilities beyond the universal ones across the character roster.
To compensate for lower movement options and emphasis on throws, it is very common for these characters to have moves to get closer and minimize projectiles. This includes examples like Zangief's Double Lariat, which is invulnerable to projectiles, and quick sweep in Street Fighter 2, which allowed him to knock down opponents consistently, allowing an approach for a throw to be more viable.
Other series have experimented with this like BlazBlue's Iron Tager who can pull opponents in with magnetism after connecting with certain moves such as Voltic Battler (even if blocked) with following moves including his powerful grabs. In exchange, he has very limited mobility options and lacks the universal double jump, air dash and forward dash.
It is also very common in more modern fighting games for characters to have Super Armor along with strong defensive tools. This ranges from the innate armor of Bowser in Super Smash Bros which lasts till he has taken too much damage to cases assigned to specific moves like Hugo's EX Monster Lariat from Ultra Street Fighter IV which can take an infinite number of hits (excluding grabs or attack with Armor Break properties).
While, it is typical for grapplers to be slow and bulky characters, there are are quite a few fast, athletic ones available as well such as Clark and Blue Mary from The King of Fighters series.