I want them to accept being handled on every part of their body without fuss, and to give their feet when asked.
I like them to lead correctly, with respect for my personal space, and to respond to poll pressure by giving and coming forward. It's ideal if they can walk, trot, halt and back at the end of the lead without lugging or coming in to my space.
I like for them to lunge in both directions at all gaits with no resistance in response to voice commands/body language and whip position.
I want them to give to pressure and step away from pressure on the ground - if I push on their hindquarter, I want them to move away, not press in on me. If I push on their shoulder, ditto.
I want them to be familiar and comfortable with a bit and bridle, understand how to give to bit pressure by flexing at the poll, and to respond to a leading rein on the ground. Basic lateral and longitudinal flexion, in other words.
The horse I just described is pretty much already broke before you get on him, you just have to put the tack on and teach him his job. I've described the ideal, but smrobs is describing the minimum necessary.
I've started horses with much less than what I've described above, but at some point you have to fill in those pieces of foundation. And it's somewhat individual. If I have a sweet, kind thing that likes people and is accepting of everything, I'm not going to be as picky about perfect response to voice command or how they jog at the end of the leadline, I'll just go ahead and get on. If I have a big, agressive, pushy colt who wants to be the alpha, I will make real sure I have everything on my list installed in triplicate before I swing a leg over.