How much time on safari is "enough" will first and foremost depend on your general level of interest, and whether you have any special interests.
You get people who think one elephant is more than plenty and prefer to spend all their free time in the disco, and those who want to live their entire lives in the bush. Most people fall somewhere between these two extremes.
Special interests such a birds, butterflies, trees or flowers give you more to look for and look at than just the big & hairy and fangs & claws, so you can spend more time in the bush without getting bored.
Location is aonther factor. Private lodges that operate on private land or in concession usually have fairly small traversing areas, so after a few days you can end up going around in circles viewing the same five sleeping lions again and again. Some lodges do have very large traversing areas, but often only utilise a small core section, with the same results.
If you visit several lodges, or travel through large national parks such as Kruger or the Serengeti, a change of scenery, landscapes and animals could keep things interesting for longer.
The diversity and abundance of animals is also important. The southeastern Serengeti (or, more accurately, the northwestern Ngorongoro Conservation Area) in January and February, when the short grass plains are studded with hundreds of thousands of wildebeest, zebra, and antelope is not quite the same experience as spending days looking for a handful of desert elephants in the arid interior of Namibia.
Finally, weather and climate can be a factor. If you choose to visit in the rainy season, you make get tired of getting soaked on game drives after the first day or so.
As a very general rule of thumb, I would suggest that for those for whom the safari will be a one-off experience, and who only want to see the big stuff, three or four nights will suffice, provided the area visited is rich in game.
Johan