I've been thinking about this lately myself. I have come to believe there are different levels of success in a startup, which could also be viewed as milestones in a way. Particular startups will only get to a certain level, but attaining any level is a success to some degree. Perhaps, they aren't really levels, because that insinuates a linear process. You can tell from this rambling that I haven't really nailed this thought down yet...I hope someone can build upon it. But off the top of my head:
Level 1: Actually make something that is functional.
Level 2: Actually have someone test it.
Level 3: Actually have someone buy it/use it for real.
Level 4: Actually have the users from the previous Level maintain their use, i.e. convert to real users.
Level 5: Get to some level of profitability.
Level 6: Make a decent amount of money.
Level 7: Make a lot of money, i.e. from an exit event or just large value of company, etc.
I know this includes financial stuff, which you specifically didn't want. However, I think this is inextricably tied to the higher levels of startup success. Obviously in the lower levels, some people may have other metrics beyond other use, like organizational metrics such as hiring employees or making something that grows beyond themselves, i.e. can be passed on.