Recommendations

While Bubblegum Crisis still tops my list of favorite anime, here are some of my other top picks of late '80s/early '90s sci-fi anime and manga. If you enjoyed Bubblegum Crisis and Crash, you may also enjoy these other classic series:

Anime

AD Police Files AD Police Files (1990) - 3 episode OVA prequel to Bubblegum Crisis which tells of Leon McNichol's early days with the AD Police. Some of the original BGC crew, including Toshimichi Suzuki, Masami Obari, Shinji Aramaki, and Junji Fujita were involved in the production.
Gall Force Gall Force (first film: 1986) - Great sci-fi/space adventure series that has spawned numerous sequels and spin-offs over the years. The first film, "Eternal Story," follows a fleet of Solnoids, an all-female race, who are on a quest to reach the planet Chaos and defend it from an alien race known as the Paranoids. A surprising amount of plot twists and turns along the way. Much of the same crew from BGC was involved in its production. Character designs by Kenichi Sonoda.
Cyber City Oedo 808 Cyber City Oedo 808 (1990-1991) - A top-notch 3 part OVA about three criminals who are given a deal to join the Cyber Police and receive a reduction in their sentences for each mission they complete. The catch? They must accomplish their missions on time otherwise their chief will detonate the explosive collars on their necks. As far as classic cyberpunk anime goes, this is a real underrated gem with excellent character-focused episodes, suspense, and quality animation.

Manga

Ghost in the Shell Ghost in the Shell (1989-1990) - Probably the most well known cyberpunk manga/anime franchise out there. GITS has been adapted in several different versions over the years, but I always find myself returning to Masamune Shirow's original manga. A superb story which follows Major Motoko Kusanagi and the Section 9 Task Force's fight against the mysterious cyber criminal known as the Puppeteer.
Appleseed Appleseed (1985-1989) - Another epic, classic cyberpunk manga by Masamune Shirow. Great mix of mecha action, memorable characters, and deep plot. Set after World War III, it tells the story of ESWAT officer Deunan Knute and her cyborg partner Briareos as they fight to save the city Olympus, the utopia of the future. Four volumes. Also adapted into an OVA and later into two CG films directed by Shinji Aramaki.