The super star (*) key in Vim will search for the word under the cursor and jump forward to the next match. The user can jump to the next matches with the n key.
The other answers here are good, particularly @rodrigo's, but I wanted to write a solution that preserves scroll position and does so without affecting any of the marks.
This works for me:
function! StarPositionSave()
let g:star_position_cursor = getpos('.')
normal! H
let g:star_position_top = getpos('.')
call setpos('.', g:star_position_cursor)
endfunction
function! StarPositionRestore()
call setpos('.', g:star_position_top)
normal! zt
call setpos('.', g:star_position_cursor)
endfunction
nnoremap * :call StarPositionSave()*:call StarPositionRestore()
Putting normal! * in the function directly doesn't seem to work, as (at least in neovim) it suppresses search highlighting from being triggered (as if :nohlsearch was run).