hi! People still ride horses without stirrups or even a saddle (riding bareback). Is there a particular culture or time-period you're wondering about? That would help the historians zero in on an answer for you.

In modern horseback riding, bareback riding (riding without a saddle) is still practiced. The romans had a 4-pronged saddle that they gripped using their thighs to hold themselves in. I've heard somewhere that the Numidians rode bareback in combat, but I can't recall where.

Here's a good image of an attempt at reconstructing the 4-pronged saddle: http://www.radpour.com/sassanian-roman-saddle

A discussion on Roman cavalry and 4-pronged saddle use: http://www.comitatus.net/cavalryrecreate.html

It's possible to gallop, jump or perform intricate manoeuvres without stirrups - your thighs and calves hug the horse all round its body, and can provide enough support even without stirrups to brace against if you're a good rider. For long-distance riding, a stirrup-less saddle could take care of the biggest comfort issue - that is, the pressure on the horse's spine (and its pressure on your crotch).