Against the Romans, Alexander would have lost. Several hundred years later, when Perseus of Macedon fought the Roman army, the Macedonians found it hard to keep the line strait and their ranks unbroken, so once there was a gap, the Romans would rush in and massacre the people left and right. The Macedonians with a ridged command structure and armed with pikes could do nothing. The gaps widened and more Romans poured in. The Romans started off with 38,000 and left the field with 1000 less men. The Macedonians started off with 44,000. and left the field with 25,000 less men.
If Alexander was given another army and enough time to figure out the strengths and weaknesses, he probably could have taken over some states. However, because politics and geography where different, he would probably not be as great.
Alexander and Macedon were a state in northern Greece, who for much of its early history, was peaceful. This left The southern Greek states unaware and unprepared for the attacks from Macedon. If Alexander was king of Athens, he might not have been as successful since all he would have had was an unprofessional army and the Peloponnese League ready to pounce on him.
It also helped Alexander that to the east, the only real enemies he faced were the Persians. By this I don't mean that the Persians where incompetent, but rather, the Macedonian army only had to adapt tactics to fight one army. They didn't have to face the Carthegenians, the Gauls, the Greeks, and the Germanic tribes at the same time (Rome). Alexander's armies used the pike successfully against the Persians. The Persians were unable to adapt to the new weapon, and so, Alexander was able to defeat them.
When Alexander faced the Indians, he had less success because he had to form new tactics to fight them. He was repeatedly crushed by the elephant until he found how cowardly the elephants were and had them run and trample the Indian lines. He also found that India's dampness really didn't suit the metal armor and arms of his Phalanx. They all rusted.
Moving on to politics: if Alexander had been made a Roman general, he would face less success. In Rome, the generals' powers were quite limited, and were always fighting for power with the senate. When a general became popular, grew his army too large, or went too far away from Rome to be governed by the senate, the senate tended to take actions to limit his power. (Think back to Caesar) With this constant power struggle, it is doubtful that Alexander would have been so great.