Persistence

Don't let anyone fool you.  Starting and running a business is work!  Things happen and setback occur.  Successful self-employed people have to be able to keep going to make the business succeed.

Self-esteem

You have to believe in yourself!  You have to believe that you can do it.  There will be times when no one else will.  You won't have a boss encouraging you (or goading you.)  You become the boss to yourself and will have to know your strengths, abilities and limitations.  You don't have to keep those limitations but you need to start out recognizing them.  And then believing in yourself.

Discipline

In your own business, you are the boss.  Money doesn't come in if the work doesn't get out.  You have to set and meet deadlines, even when you are tired or would rather take the day off.  You have to find the motivation to make it happen.  Sometimes, you have to "just do it".

Resourcefulness

Challenges arrive in life.  Even more so in your own business.  There won't be someone telling you how to handle each challenge, each crisis.  You will have to do your own thinking and problem-solving.  Sure, there are resources to help you.  But they won't come to you and tell you what to do.  You will have to seek them out.  You will have to find ways to apply someone else's solution to your problem. 

Networking

This is not talking about computers but about your network of friends; associates; extended family and relatives; neighbors; and your current and former coworkers.  This can also include people you know via the internet.  Later on, this will include your customers and former customers.  You don't have to be a "glad-handing" salesman "working the room" to succeed in your own business.  But you will need the help of others to get started, to provide referrals and testimonials, and to generally give you encouragement and support.  If you can't bear to interact with people—even a little bit—(this can be by computer as well as in-person or by telephone), then you may not be suited for owning and running a small business.

Passion

When it is your business, you live with it around the clock, throughout the year.  If you are going to do that, you need to have a passion for it or it quickly becomes something you will resent, then hate.  Or you will become indifferent to it and that will kill the business just as well.  So, in addition to believing in yourself, you must also believe in your product, your service, or in what you are doing.  And if you have several passions, making it hard to choose just one?  Consider building your business around two or more of them.  It has been successfully done before.

Industry Knowledge

You need to have a working knowledge of the area or industry of your business.  If you don't already have it, then don't open your business, yet.  Get the knowledge you need, first.  That said, it doesn't mean that you have to become an expert in the field before you can start.  But you should know what you are doing and what you are getting into before you "hang up your shingle".  In the old guild system (and still seen in the trade unions today) this was graduating from apprentice to journeyman.  You still had plenty to learn and skills to hone, but you were recognized as qualified to be an independent worker.  Make sure that you have enough skills to keep the business open once you start it.