Hector the Bulldog is a bulldog, usually the pet of Granny. Normally he clobbers Sylvester so he won't eat Tweety. He is muscle-bound and has grey fur (except for "A Street Cat Named Sylvester" and "Greedy for Tweety" where his fur is yellow-ish.)
Hector's possible debut appearance in the 1945 short "Peck Up Your Troubles" paired with Sylvester and a woodpecker. His second appearance was in "A Hare Grows in Manhattan". After that, Hector was a minor player in many Sylvester & Tweety cartoons, including 1954's "Satan's Waitin'".
Outside the Tweety cartoons, Hector is usually also Sylvester's arch-enemy (such as in "Little Red Rodent Hood", "A Kiddies Kitty", "Pappy's Puppy"). In one cartoon in particular, "Stooge for a Mouse", both Sylvester and Hector (known as "Mike") start off as friends, but turn into sworn enemies thanks to a mouse Sylvester had chased earlier. However in the first two Sylvester/Hippety Hopper cartoons, "Hop, Look and Listen" and "Hippety Hopper", Hector often insists Sylvester catch the "giant mouse" for his (Sylvester's) own good.
Hector is essentially not the same bulldog who paired with Chester in two Sylvester cartoons ("Tree for Two" and "Dr. Jerkyl's Hide"). Similarly Chuck Jones' famous bulldog who paired with Pussyfoot, Marc Anthony although bearing a close resemblance to Hector, is not the same character either.
He also has a role in the series The Sylvester & Tweety Mysteries, where Sylvester is constantly outwitting him. He also made a cameo appearance in Tweety's High-Flying Adventure, and appears in the Webtoon, "Full Metal Racket!"