A person without squares in his natal birth chart would signify that he may be into any of these situations: no heavy stress in life, no great challenges to face, no opposing forces, no opportunities for improvement, and no chances for resolution of conflict may be experienced to
Molly Hall from About.com:Astrology says that the "negative" aspects found in the birth chart can point to areas of great challenge or difficulty. These are called squares and oppositions because of their relationship on the birth chart wheel. Therefore, a birth chart without a square could mean the following:
No heavy stress in life
Stress is a part of human existence be it in a good or bad way. If no square is found in your birth chart then you are lucky enough to avoid stress that are burdensome to your relationship to others, your lifestyle, your career, and health. You can live your life without having to go through the ill effects of stress for you only encounter light ones. This will deeply affect your mood and disposition in life as an advantage of a stress-free living. Also, your sense of well being is better than most.
No great challenges to face
You will not encounter challenges to every aspect of your life. Hardship is not one you are familiar with. You live your life with ease and comfort. This is very helpful in building new relationships, pursuing a career, and maintaining your health as this is of no difficulty for you.
No opposing forces
It is more likely that you get what you want or desire. You will gain more confidence as you act upon things without struggle. It's like you are a well-oiled machinery wherein you go on about your life with little friction or troubles.
No opportunities for improvement
Without great challenges going your way, you do not have much opportunities to become a better person. It is probable that you lack growth and has the tendency to be stagnant in your ways. You cannot experience stimulating events that help you improve your knowledge, attitude and skills.
No chances for resolution of conflict
The downside of not having conflicts is that you can not improve your problem-solving skills. Your resilience is not tested and you are likely to become vulnerable to tough elements. You do not have the chance to become a stronger and wiser individual.
These are just possibilities and should not be considered as inevitable. You can change everything with just one decision. I think that you create your own destiny and not the stars. I believe that the stars only serve as your guide. Therefore, don't think that your life is written for you because in reality, it is you who holds the pen.