After LogMeIn screwed over their free customers, and even paid customers who bought their apps, I have put together a list of alternatives.
[Free for personal use, Pro for business] Probably the best out there. They have apps for Windows/Mac/Linux, and iOS/Google Play.
Google Chrome Remote Desktop Requires Google Chrome. Windows/Mac/Linux, Mobile apps in the works.
[Free and Paid versions] Windows/Mac/Linux, iOS/Google Play ($9.99 but sometimes free)
TightVNC [Free for Personal or Business use] Open source! Windows/Unix platforms
GoToMyPC by Citrix [Paid, Free Trial] Windows,Mac,iPad & iPhone,Android,Kindle Fire
Mikogo [Free for Private Use]
iTeleport [Paid] Windows, Mac, iOS, Google Play (coming soon)