The earliest Buddhists did not portray the Buddha in human form, perhaps as a sign that he had transcended the condition of birth-and-death that marks embodied existence.  Instead, they portrayed the Buddhis using a series of symbols associated with key events in his life: a lotus (or elephant) for his birth, a tree or throne for his enlightenment, a wheel for his first teaching (the Four Noble Truths), and a stupa (funerary mound) for his bodily demise.  Another common symbol is a pair of footprints (see below).  The carvings at Sanchi have numerous examples of such aniconic portrayals, such as this one in which the Buddha (the tree) is surrounded by respectful devotees, both human and celestial.  

The tree stands for the Buddha's enlightenment, the pivotal event in his spiritual career.  According to tradition, the Buddha renounced his home at the age of 29 and spent the next six years testing various teachings and spiritual disciplines (most notably strict fasting) to find the solution to old age, illness, and death.  All were unsuccessful, but then he sat underneath a ficus tree in Bodh Gaya (modern Bihar), and began to meditate on the question of birth-and-death with a focused mind.  His analysis eventually revealed the causal chain that leads to rebirth, known as pratityasamutpada ("Interdependent Origination"), in which each element provides the cause for the one that follows.

This image of the Buddha receiving offerings from devotess (pouring water at the base of the tree) comes from the Cleveland Museum of Art.

The wheel symbolizes the third great event in the Buddha's life, in which he "turned the wheel of dharma" by preaching his first sermon (The Four Noble Truths) at Sarnath, just north of modern Benares.  If the tree represents the enlightened being, the wheel represents his career as a teacher. 

To find suitable hearers for his message, the Buddha walked 150 miles from Bodh Gaya to Sarnath during the hottest part of the year, in which the mercury goes over 110F every day.  Tradition relates that the Buddha was initially reluctant to teach others, since he doubted whether anyone would understand his message, but traveling this distance in such blistering heat testifies to the strength of his resolve.

This image depicts the miracle of  Shravasti, in which the Buddha first created multiple images of himself and then flew in the air.  Here the Buddha appears as a stupa, a dome-shaped mound that mimics the funerary mounds of great kings.  The earliest stupas enshrined the Buddha's physical relics (bones and teeth), and thus affirmed his royal status, but the relics also gave people continuing contact with the Buddha himself.  Although after his enlightenment Buddha was free from rebirth, his body was like any other human body.  At 80--an enormously long life for that time--he got food poisoning (either pork or mushrooms, the text is ambiguous ), got dysentery, and died of dehydration (the story is so inglorious that it is more likely to be true).  Tradition reports that stayed composed to the end, blessed the man who fed him that meal, consoled his disciples, and directed them to inter his remains in a stupa.

This small image from the Sanchi stupa's eastern gateway may represent the Buddha's birth (his mother's cooling bath after the delivery).  Elephants appear in the story of the Buddha's conception, in which his mother became pregnant when a white elephant appeared in a dream, and tapped her abdomen with the lotus it was holding in its trunk.  Traditional accounts of his birth highlight miraculous elements: the Future Buddha emerged from his mother's side, rather than a normal delivery; upon hitting the ground he took seven steps toward the east and proclaimed that he would be enlightened in that lifetime, and there were various supernatural signs--rain and flowers falling from a clear sky, melodious sounds, disabled people regaining their faculties, and many, many others.   His birth is traditionally believed to have occurred in Lumbini in southeastern Nepal.

The final symbol is the is the footprints of the Buddha.  This image comes from Sanchi's east gate in a panel depicting him renouncing his home and family to seek a solution to birth-and-death.  He left home on a horse, seen at top taking him away (note the royal umbrella) -and being led back riderless at the bottom; in the center is a devotee paying homage to the Buddha.

Footprints directly connect a past event (making the footprint) with one's present experience (seeing the footprint).  Even though the Buddha final nirvana some 2,500 years ago, the "traces" of his life remain vibrant through his teachings; the Theravada Buddhist segment in The Long Search film series was appropriately titled "The Footprint of the Buddha."