If there were no equids at all, the whole course of human history would be much different.
If there was just no Caballus ferus (wild horse)... well, probably other equids would have been domesticated. Zebras and even kiangs can be domesticated, simply horses outcompete them in most applications.
There are just too many possibilities to tell what exactly would happen, but I second the view that horse was much more important to communication than transportation or agriculture.
Looking at communication - primitive heliograph was known around 400 BCE, and then there were smoke signals and stuff like that. Horse messenger turned out to be simpler and more reliable, but, if there were no horse messengers, these technologies could see more development.
Another thing is, clocks would probably have been invented later and would not be as widespread.
No, seriously. What purpose is there in measuring time if you cannot arrive anywhere when you want because that's your donkey who decides how fast you'd move along? Even to this day, civilizations employing donkeys and other animals more stubborn that horse don't care much about time.
And then there is this fine idea...
(Pictures from
here)