Evren's answer is excellent! To add on, Coltrane's "Countdown" and "Giant Steps" are good examples of music that doesn't require a key signature because the key changes so quickly and so many times throughout the form. However, there are plenty of types of music that don't adhere to keys at all, in that they are not tonal in a way that can be analyzed by the Western tradition. For example, Arnold Schoenberg famously rejected traditional tonality and created tonal systems of his own to adhere to when composing. Several forms of the blues, as we know it today, aren't really in any key at all since every chord is dominant, and so assigning a key would be missing the point. There are endless examples of music from around the world that divide an octave up into far more than 12 notes, making Western keys irrelevant in those contexts. I encourage you and everyone to dive deep and widen your musical horizons. Western music is only part of the story. Hope this helps!