Amateur radio operators still use Morse Code, as do a few other government services, such as aviation beacons, etc. These Morse Code signals are usually just encoded text (roughly related to other text encoding schemes such as ACSII or Braille).
Morse code allows an extremely simple on-off transmission scheme (about as simple a modulation as can be done). Letters and numbers can be encoded into sequences of long and short on-off signals, each character having a specific pattern in time. Originally it was thought that these time sequences would have to be graphically charted out and read, or translated by some sort of machine. But it turned out that after hearing it for awhile (and learning the distinctive sound of each letter) telegraph and radio operators could understand (and type out for telegrams, etc.) the Morse Code encoded messages just by listening to the relay ticks or the radio sidetones.
So, yes, if you learn what all the letters sound like (fast enough, which takes a bit of practice), you might be able to understand the message just by listening.