Weird means 'very strange' or 'bizarre' in dictionaries. Its synonyms include words like outlandish, quirky, eccentric, idiosyncratic, surreal, peculiar, odd, zany, madcap, freakish and crazy among other things. So it's a given that 'weird' will mean different things to different people.
For the sake of this list, let's go towards the more outlandish and bizarre end of 'weird' and focus on the less well known films and directors, which means there's no space for Jodorowsky, Lynch, Cronenberg, Bunuel, Gilliam, Takashi Miike, Peter Greenaway, Guy Maddin, Waters or even golden era Hollywood comedies like Hellzapoppin' or anything with the Marx Brothers. These guys are famous enough as it is and you can always read about their films somewhere.
What this list hopefully tries to do is to bring to your attention the less heralded films that fall under the 'weird' banner, or even some relatively well known ones you didn't realize was actually quite weird and insane.