The busiest tourist season for Egypt runs from November to February, because it's seen by most people as the best time to visit (weather, climat are quite soft). The peak months are December and January. The Nile Valley is pleasant on winter season, Cairo could be quite chilly. Sinai resorts are the most busy during the winter, while Hurghada is active all year around. March or April are good months to visit Egypt too, because climate is still pleasant, but it's better to avoid Easter vacation time, when resorts could be flooded with tourists.
Heat is still tolerable in May, but it really depends on a year, so rich enough locacls prefer to move to Alex and coastal resorts. June - September period is the most hot and unpleasant season, pollution in Cairo is highest during this time and the only way to hide from heat is coast.
The best combination of climate and tourists amount is perhaps October to early November.
Not only climate can effect your travel. Islamic calendar and its related festivals can change your plans. The most importnant is Ramadan, which can reduce your possibilities for eating and transport.