Another way:
ggVGJ
"ggVG" visually selects all lines, and "J" joins them.
ggVG
J
Ah, I found the answer.
:1,$join
Works like a charm.
EDIT: As pointed out in the comment:
:%join -or- :%j
...removes the range.
You can do it with 3 keystrokes starting from normal mode:
:%j
:
%
j
Now it seems that this adds a space between the lines. I am not sure if you want this.