I'm still typing myself, since typing with mental illness is a little tricky:
-Edward Elric and Maes Hughes from Fullmetal Alchemist
-Beetlejuice and Delia Deetz from specifically the "Beetlejuice" musical adaptation
-Cecil from Welcome to Night Vale
-Stolas and Blitzo from Helluva Boss
-John and Allison from Breakfast Club
-Bill and Ted from Bill and Ted's Excellent Adventure
-The Dude from the Big Lebowski
-Klaus and Number 5 from The Umbrella Academy
-JD and Veronica from Heathers
Naturally, there are parts of this where I can see my mental illness coming out more (namely Allison, John, Blitzo, Beetlejuice, and JD). Of course, those are still characters that I relate to, even if they're mental illness related. How mental illness alters the personality isn't commonly discussed; I've seen a lot of online forums that just want to say "This character is psychotic; There's no point in typing them". As someone affected by a psychotic disorder, I wish this was more discussed rather than brushed aside.
(NOTE: Psychotic disorder does not necessarily mean psychopath. It can typically hint to psychosis, which can be any number of things, namely disorders that include hallucinations and delusions, which can occur for any number of reasons.)
(DOUBLE NOTE: Just because I relate to characters that are known for crossing boundaries like climbing in someone's window, invading someone's personal space and deliberately manipulating them, and even committing unaliving of others does not mean I will do those things to others around me. I'm not gonna go trying to wreak that kind of havoc. We don't accept that kind of behavior around these parts.)