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Pro Easy setup
TeamViewer has been around since 2005 with an excellent track record.
Pro Free for personal use
As long as you don't use TeamViewer for commercial use, it's free.
Works on Windows, Linux, OS X, iOS and Android. Works seamlessly independent of platform and accessible for web, mobile, and desktop app usage.
Pro Multiple remote sessions
You can connect to multiple computers at the same time and navigate them via tabs.
Pro Two-step authentication support
In tandem with TeamViewer mobile app, you can choose to set up two-factor authentication.
Pro Clipboard passthrough
Things that you copy to your clipboard (ctrl + c), can be pasted on the remote computer (ctrl + v).
Pro File sharing
You can transfer files over TeamViewer simply by dragging and dropping.
TeamViewer has the ability to wake up a sleeping computer and return it to sleep state on disconnect.
Pro Can designate users that can always connect
Has option to give permission for someone to remotely connect with or without being granted.
Con Compromised leading to many users having their personal information stolen
Users are reporting that TeamViewer has been compromised, leading to these users having their personal computers and browsers used in a remote session in order to purchase copious amounts of online codes.
Each time the application is in the process of being closed it stops to try to sell you the paid version.
Con Linux version's performance could be better
TeamViewer is powered by Wine, an emulator, on Linux and as such it runs slower than a native application would.