Well, no. you don't need them, but they serve there purposes. A lot of content on the internet relies on Flash Player, some what less so on Shockwaves but there are some sites that rely on it.
answered Jan 18 at 15:37
There are a very few things in life you actually need but in terms of comfortable use of your computer you should have Flash installed yes. There's all sort of talk about HTML5 replacing it but we are nowhere near there yet.
Shockwave is an antique I don't think is used anymore. I don't have it atleast, nor have i stumbled on a reason to install it. Not for years.
Noone can really tell you what you need. If you require a tool do accomplish a task you need that tool. Its simple really. :)