I am a Sagittarius, born on the cusp of Scorpio. Wikipedia defines the characteristics of Sagittarius this way:
Sagittarius is seasonally associated with the transition from autumnal moisture to mid-winter dryness. Because its period indicates a change of season, it is known as a “mutable sign” :88 describing an instinct toward change and an easy ability to modify or adapt to the demands of the environment.
The sign is governed by Jupiter, a planet which is symbolically associated with temperate qualities which loosen, relax and expand. Sagittarius is also linked with the “element of fire,” which represents outgoing, action-oriented energy that seeks spontaneous expression.:46 As the mutable fire sign, governed by an expansive planet, the symbolic focus of the sign is connected to the principle of exploration and evolution. Correspondingly, Sagittarians are reputed to be drawn toward travel and philosophy, and to enjoy social contacts, meeting new people and exploring other cultures. They are said to be highly intelligent, broad-visioned, tolerant in their views, mainly concerned with the “big picture” but with little patience for the details.:71
Joanna Watters (2003) defined a key phrase for this sign as “I seek” and describes Sagittarius as “the sign of the higher mind … the pursuit of wisdom and search for meaning are just as important as new places and experiences”.:24 Like all the fire signs, Sagittarius can be idealistic in vision but tactless in expression. They are known for their bluntness yet are often unaware of their ability to cause anguish in others.:24
Sagittarius keywords: philosophical, optimism, expansion, farseeing, anticipation, direct, idealism, pride, restlessness, freedom-loving.
I do love travel and learning about other places and people, though I am more of an introvert (the Scorpio part of me). I am philosophical and idealistic, and unfortunately I do cause people anguish without meaning to. I am restless and do love my freedom.
Since I was born on the cusp of Scorpio, I also exhibit characteristics of Scorpio, which Wikipedia defines this way:
According to Alan Leo, generally considered to be the founder of modern psychological astrology and sun sign astrology, people born with the sun in Scorpio are “very determined, reserved, tenacious and secretive. They are firm and somewhat proud, and capable of unmistakable traits of character that cause them to be either very much liked or very much disliked. Their somewhat suspicious nature causes them to be distrustful, but amidst all their apparent evil traits of character, they have that grit and backbone which enables them to make higher attainments than those born in the other signs ; For the “wisdom of the Serpent” lies concealed in this sign, and they become so discreet. wise and prudent as to display extraordinary genius. It has been said “the greater the animal the greater the man,” and it may be that in the animal passions there lie the germs of the spiritual force, which, when sent upwards, may achieve great and mighty things. That which seemed latent will and desire in the sign Taurus becomes, in this sign, expressed energy. The Scorpio desires are potent and charged with the power to attain the object of their desires; but when their desires are subservient to the will, there are none more powerful or determined. In conclusion, it may be said that the Scorpio individuals that they have reached the point that they decide their own future progress. 
Scorpio Keywords: Intensity, determination, magnetism, powerfulness, emotion, intuition, secretness, self-reliance, rebirth, penetration, jealousy, introvertion, resourcefulness.
The characteristics of Scorpio that I have are that I am an introvert, emotional, secretive, self-reliant, jealous, and resourceful. I am also very intense about certain things.
Living on the cusp brings the best and worst of two worlds.