The short October/November and March/April rainy seasons notwithstanding, the Serengeti's temperate and mostly dry climate plus abundant resident wildlife makes for a great game viewing experience all year round - the question of exactly when to go to the Serengeti really revolves around whether you want to see the wildebeest migration.
If so, then the best time to visit the Serengeti is between October and July before the wildebeest return to Kenya's Masai Mara around August. Note however that the migration is a fluid affair: not only is its precise timing subject to each year's rainfall pattern but the herds move around the Serengeti depending on the time of year.