Looney Tunes Comics refers to a number of different comics, published by various companies since 1940.
The first company to publish Looney Tunes comics was Dell Publishing in 1940. Originally titled Looney Tunes and Merrie Melodies Comics for the first 165 issues, the name was shortened to just Looney Tunes in 1955. Additionally, Bugs Bunny, Daffy Duck, Porky Pig, and Tweety & Sylvester all appeared in the Dell Four Color comic book, before each getting their own title. The Road Runner also received his own title, simply called Beep Beep. Dell ceased publishing all these titles in 1962.
Gold Key / Whitman
In 1962, the Gold Key line picked up Bugs Bunny. Within a few years they brought back Daffy, Porky, Tweety & Sylvester, and Beep Beep, and even gave Yosemite Sam his own title. They also starred Taz in the short-lived Tasmanian Devil and His Tasty Friends. But it wasn't until 1975 that they restarted the Looney Tunes title. All the titles (except Taz's already defunct one) survived when Gold Key transformed into Whitman, but some just ran reprints instead of original stories.
Today Looney Tunes comics are published by DC Comics, with a variety of different artists working on them. They tried a Bugs Bunny Monthly and a one-shot Taz special before the current long-running Looney Tunes series. DC also published an Animaniacs title for a few years.