Adobe Flash has been a popular target by hackers for a very long time because it's widely used and almost never kept updated by so many users. Using Adobe Flash as an attack vector is a great choice because they can affect anyone, regardless of what operating system they are using just by just installing malicious code on a website. Flash exploits seem to be a monthly occurrence, which means anyone using it must stay focused on keeping it updated.
There was a time that much of the animation and graphics on the Internet required Flash, so not having it made a lot of websites useless. This is no longer the case today as newer standards such as HTML5 are helping to reduce the need for Flash, but depending up on your surfing habits, it still may be necessary.
Some websites will appear to have gray boxes with a puzzle piece to indicate that Flash is necessary. If you hover your mouse over the box, it will give you information about what is missing.
Removing Flash is the best course of action to take and it is much safer, but you may need it for some sites that you frequent. A good way to test and see if you need it is to remove Flash. First completely uninstall Adobe Flash Player from your system. For Windows you can go here and for Mac OSX you can go here. Once you have uninstalled Adobe Flash you should decide which browser to use as your main safe browser. For Mac you can use Safari and for Windows you can use Internet Explorer.
When you visit a website that requires Flash that you absolutely need to use you should make a note of it. If you feel that you truly cannot live without that website and are willing to risk your security to use it then go ahead and install Adobe Flash. Also install a second browser like Firefox. What you will need to do is make sure that Adobe Flash is disabled in Internet Explorer or Safari. Then make sure Adobe Flash is enabled in Firefox. Firefox will be your non-safe browser that you should only use for the specific websites that you need to use that require Adobe Flash.
Chances are that you will find that Flash isn't critical for everyday use. If you do keep Adobe Flash installed on your system then make sure you keep it updated constantly.