FLCL, Top wo Nerae 2! Diebuster Recommendations
Same director, same style and the same over the top action. Both titles feature crazy mech designs and similiar humour.
Honestly I had a hard time thinking of an anime that was similar to FLCL, since it stands out from the pack so much. I didnt quite get the same feeling from watching FLCL as I do from watching Dead Leaves or TTGL as suggested by the top suggestions. I finally settled on Top wo Narae 2 being the closest to FLCL. It seems to have the same sort of crazy comedy and over the top action as FLCL. Even though they aren't quite the same, this was the closest I could
Another 6 episode OVA by the same studio and director, which shows through very clearly in the animation style. The plot is more comprehensible but it follows FLCL's practice of showing first, and explaining later, so many things only make sense in hindsight.
It's highly recommended to watch Gunbuster (Top wo Nerae!) first, as Diebuster builds off the plot of its predecessor.
Same director and writer so they have a similar style. They have similar themes about growing up, phenomenally exciting robot action, and fantastically expressive characters; the two main heroines of Diebuster also resemble Naoto and Haruko in that one is rather cynical while the other is hyperactive (and has pink hair) and they also have a bit of a romance. Both have a similar pacing as well, with the first three episodes focused mostly on the characters and the last three episodes being more plot-centric.
(Diebuster is a sequel to Gunbuster but they're both quite short)
Diebuster is what you would get if FLCL had a baby with the original Gunbuster anime. Both have the same director and writer as well.
Both works are directed by the at the time Gainax animator Kazuya Tsurumaki. Each show is characterized by kinetic action, narrative density, strong characters, and fluid animation. Both works are insane in a way that only a Tsurumaki work can be, though it should be noted diebuster has a much easier to follow narrative.