For example, suppose you play an F and an F#, or a B and a C, from the same octave at the same time. It usually doesn't sound very good. I've looked a while but I can't seem to find a name for it. Is there a name?
Generally you would call these intervals minor seconds. But depending on the "spelling" of the notes you could call the interval an augmented unison.
B and C is a minor second
F and F# is an augmented unison (the letters are the same so it is a unison to start, then the sharp on the second F augments it by making it 'bigger' by a half step.)
These intervals are considered dissonant and harsh sounding.