For moving directly vertical:

:nnoremap k gk

:nnoremap j gj

These move up/down one character, even if it is the same line wrapped over. Really beneficial for things like LaTeX editing.

I was going to say. Disabling hjkl makes moving between word wrapped lines impossible

If you want to go to the same cursor position on the next line, definitely j is the way to go.

Much of the time, I want to go to a specific part of the next line. In which case, let's say I want to go to the parse function, I'll do "/par<enter>".

+

and - to move 1 line up. Combine with a number, 4+ to move down 4 lines, complementing 4G or :4<CR> to move to 4th line.

I don't see those as an improvement (i.e. worth committing to muscle memory) for `j` and `k` that would incentivize me to no-op those two keys. You can do `4j` as well.

I use {} for moving paragraphs at a time. And HML for switching to top, middle or bottom of screen.

using '/' (search) comes to mind. Drew also did an episode cover some more ideas and touches on relative number moving. http://vimcasts.org/episodes/long-range-line-duplication/