If you have this program installed (and chances are that you do) it is strongly recommended you do not use it on content you cannot for sure verify as safe.
Awhile back, researches had discovered and reported a ton of bugs (many of which can be used by attackers to introduce malware on your system) to Adobe. While Adobe has recently published a patch to combat some of them, they did not cover all of them by their update rollout. The researches who submitted them did not like this and are likely to post the specific details of the vulnerabilities out in the open. Many attackers can use that information to build malware to exploit it tremendously.
Since Adobe Reader is cross platform, all major OSes (Windows, Mac, and Linux) are equal targets for attackers.
The Google Chrome browser and the current beta version of Mozilla Firefox (as well as Aurora, Nightly, and UX) have native PDF viewers that can be used as good alternatives (you can set PDFs on your computer to open in the browser). If you're on some version of Windows 8, you can use Modern Reader. If you're on Linux you can easily find some FOSS program to cover your needs.
[Edited by Neo7, 8/17/2012 3:28:00 PM]
Flash is a proprietary format exclusively owned by Adobe. As long as there is content that requires Flash, you will need Adobe Flash. HTML5 is starting to show some promise in replacing a major component that Flash provided which is video and audio on the web but it's still a long way from doing a full replacement. Even with that there are many developers out there that have weak skills with front end work where Adobe Flash simplifies the process tremendously for things outside of video/audio.