Metrics? Awards? Freedom?
I'd suggest that there is no "should". The beauty of being an entrepreneur is that YOU get to decide what success is.
In fact - In the system I use with entrepreneurs you learn to define "success" for yourself and build it into the requirements of your business model.
The words freedom and should don't usually go hand in hand :) For me, success has always been defined as creating my personal lifestyle. I can't even say that is the right answer for anyone else but if you can sleep at night knowing you are helping solving problems for other people and making money. That COULD be defined as success right? Would love to chat more if you're interested.
I like David's answer..."Shoulds" are part of the reason many of us became Entrepreneurs.
The definition of success is completely based on your goal and objectives.
Before deciding how to measure success, you must define what it is for you and your company. Is it purely a monetary number? Is it related to company culture or charitable impact?
I have clients for whom "success" is not about money at all. Thus their measurement system is completely different than one connected to numbers.
My question back to you is: What is your primary goal for your company? How will you know when you've reached that goal?
Simple - Did you achieve your goals?
It depends on the goal you set up for yourself. Consider that success could be measured in financial terms (profitable business), from a human and learning dimension (did you grow as a person, did you learn), or from a social perspective (did you grow your network, relations that will help you in future ventures). There are probably more ways to define that, but for myself, I certainly consider the human dimension and the quality of the journey you go through as important success criteria.