Garfield Logan is the son of two biologists who were studying in South America. One things they were studying was a rare disease that made monkeys turn green, and to humans the disease was fatal. When Garfield was bitten, he almost died if it wasn't for his parent's experimental vaccine, which not only saved his life but turned him green and allowed him to turn into any animal. (Unlike the cartoon, he could speak while in animal form.) After his parents died he became a member of the Doom Patrol, and after leaving them became one of the stars of the 80's New Teen Titans.
Gar is a pretty cool character. The reason he's usually one of people's favorite Titans is mostly because he was funny. He added humor to a mostly dark book, and his storylines usually went into interesting and heart-breaking territories. I still need to go back and read the old 80's Titan stuff, but from the Geoff Johns era Titans Beast Boy was still a valued member of the team. Well, for a while anyway. I definitely recommend that era of Titans, and quite a few series with him involved.