Well, there is ; to repeat the last move in some cases.
There is the . to repeat last change.
But if I just did za or @a, is there a way to repeat it? I guess such a mechanism should ignore plain movements.
for example, I have a mapping such that H does o<ESC>D, or new line.
If I do . , it only repeats the D. So, to do so just for defined mappings would be a start.
I am almost certain that there is no way out of the box.
. repeats the last change, and usually does what you want (combine with e.g. cgn for a great sequence). For registers, @@ repeats the last register. @: repeats the last ex command. This is particularly handy with :normal! or :global.
For mappings, I use repeat.vim. You (and plugin authors) can have mappings take advantage of it so that . works as expected.
As you've noticed, the ft family of motions can be repeated with ,;. The only other 'repeatable' motion I'm aware of is /? searches via nN.
In general, certain commands don't have a repeatable version. For example, it doesn't make sense to have a builtin to repeat za, because (a) it's two characters ; (b) it doesn't edit text ; (c) it's easily mappable.
