Fedora does not include any software that doesn't meet Fedora's strict licensing guidelines on Free and open source software. Third party repositories may contain software that has non-free licensing or patent encumberances. Use them at your own discretion.
If you are looking for the Adobe Flash browser plugin, refer to the Flash page.
For Skype, refer to Skype
For Chromium or Chrome web browser, refer to the Chromium Fedora wiki page.
The following repositories are popular and commonly used by end users and do not conflict with each other
There are a number of other repositories listed below but many of them are known to explicitly conflict with each other and hence not recommended unless you are a power user and know the technical aspects better.
Mixing third party software repositories
Mixing a lot of third party repositories is not recommended since they might conflict with each other causing instability and hard to debug issues. If you are not a technical user, one safer method is to not enable the third-party repo by default and instead use yum --enablerepo=repo-name when installing packages from that repository or a similar method configurable in the graphical package manager. There are a number of yum plugins for setting repo priorities or protecting the base packages from being obsoleted by third party repositories which are helpful to more technical users