The best time to go is largely dependant on the aim of your safari. If you are looking to see the greatest concentrations of wildlife, then the drier months of June-October are generally regarded as the best time.
However, you can travel to Africa at any time of year and have an incredible safari experience so long as you go to the right areas and the right camps, with the right people.
South Africa and Namibia offer fairly consistent game viewing and safari experiences throughout the year.
Click on When to Go and choose a month from the drop down menu to see the safari conditions at that time of year.