Cancer hasn't suddenly "popped up". There is a greater chance of it occurring in an individual now due to longer lifespans and the increased range of carcinogenic factors, but it has always been with us.
There's not actually any 100% compelling evidence that AIDS is new either. It was recognised as being caused by a virus in the 1980s but could have been active long before then, with victims' deaths being notched up to their "non-responsiveness" to the treatment of whatever opportunistic disease killed them.
The other diseases you mention have not appeared and disappeared in series. The reason many of them "peaked" at different times historically is because their optimum habitats are different. Conditions that favour a massive outbreak of small pox, for instance, might not be favourable for cholera. Microbes that cause extreme damage to us are usually well-adapted to a specific habitat, and can be expected to be competitor-intolerant within that habitat.