You may have seen the Youtube video of the two senior citizens proving they can send a message faster with Morse code than teenagers can texting via cell phone. NBC keeps taking it down but this link may work for a while.
Morse Code-Leno - More bloopers are a click away
So that looks pretty fast in the video. But how fast can an operator, competent in Morse code send and receive a message? First of all let's cover how speed is calculated. Most common is the PARIS calculation. it breaks down dots and dashes this way. I'm quoting from Wikipedia for simplicity since everyone else seems to have. "Each dot is one element, each dash is three elements, intra-character spacing is one element, inter-character spacing is three elements and inter-word spacing is seven elements."
By that measure the word PARIS is exactly 50 elements. This simple set of rules makes for a consistent yardstick. There is another method called CODEX which is based on random strings of 5-letters and 60 units of time. (I'm skipping this since I cant find any source that actually uses it.) A skilled operator often can send and understand code in their heads at speeds over 40 WPM. The worlds record is significantly higher.
According to The Guinness book of world records, the world's record for Morse Code speed was set in Asheville, NC in July 1939 by Ted R. McElroy. He was clocked in Continental Morse Code with witnesses at 75.2 WPM. (Adjusted for the modern PARIS standard, that would be 72.2 wpm). His record still stands today. The record hasn't been broken in over 70 years. Ted also carries separate records for American Morse code and Japanese Kanji code. Just to rub it in he also claimed that he could type at 150 WPM. [In 1993 Tom French published a comprehensive book on the man]
Ted R. McElroy is an interesting character. He'd been using Morse code since he was a kid, and by the age of 15 he was a telegrapher for Western Union. He started and his own company manufacturing Morse code keys in 1934. That record he set in 1939 beat his own previous records set in 1935, and 1922. Between WWI and WWII McElroy worked for WCC / WSO, one of RCA's transoceanic wireless stations. More here. His McElroy manufacturing Corporation made Morse code keys for decades and made millions during WWII. After the war things slowed down and in 1955 he sold the company. He died in 1963.