Join lines inside paragraphs in vim
I think this does what you want: make sure there is an empty line at the end of the file, then join every paragraph (terminated by an empty line).
G:a
.
:g/^./ .,/^$/-1 join
Explanation: first go to the end of the file and append an extra empty line with :a (maybe there's a more elegant way to do that; interactively, you can replace the first three lines with o<ESC>). Then, for every non-blank line that hasn't been considered yet (:g/^./), apply the join command to the range starting at the selected line (.) and ending one line before the next empty line (/^$/-1).
Optionally, :g/^$/d if you don't want any blank line to remain (then you can take off the -1).
This should do it:
:set tw=99999
gggqG
tw is set to some value at least as large as the number of characters in the longest paragraph. gg moves the cursor to the first line; gq is the command to reformat; G moves the cursor to the last line, telling gq to reformat from the current cursor location to the last line.
Set the cursor inside the desired paragraph
Type:
vipJ
(vip highlights the current paragraph, J joins all lines)