How to break a line in vim in normal mode?

Try this:

:nnoremap <NL> i<CR><ESC>

then just press Ctrl-J whenever you want to split a line.

I don't know of a single key command, but a lot of times I do "r" then "Enter" to break a line.

"r" replaces the current character under the cursor without going into insert mode. This may not be what you want if you don't want to replace a character...

put cursor in position and...

  r<Enter>

Similar to other answers but doesn't replace the current character.

R<enter>

No remaps required.

As far as I know this isn't possible without entering insert mode. You can however macro it with something like (replace Z with whatever key you want to use)

nmap Z i<cr><esc>k$

basically this maps the key 'Z' to enter insert mode 'i', insert a carriage return '<cr>', leave insert mode '<esc>', go up a line 'k' and finally go to the end of the line '$'