As the question states, I primarily use OSX (Mountain Lion), but have a Windows 8 installed on a separate machine. How do I remote desktop into my Windows 8 machine from OSX?
I use a powerful, and very secure cross-platform (windows, OSX and iOS, linux) program called TeamViewer. It does remote control, meetings, VoIP, text-chat, VPN, file transfer, LAN connection (uses LAN instead of internet for higher speed; requires both computers to be on same network) and there's probably another feature or two I've forgotten about (it's full of features!). It requires no fiddly configuring ports and firewalls and works on non-administrator accounts.
For the record, I've never had any security issues with TeamViewer. It is also free for non-commercial use (commercial license is very expensive (on the order of several hundred AUD), but you haven't said it's for work, so I'm assuming its for non-commercial use).
I suggest that you use TeamViewer
One option is FreeRDP. I believe it is somewhat more fully featured than the Microsoft client.
A simple, intuitive program that implements the RDP protocol is CoRD. It is also free and open source. I use it to manage a Windows Small Server at the office and it is the simplest RDP program I've tested. Hope it helps.
The Microsoft Remote Desktop Connection Client was not updated to work with OS X Mountain Lioan (v10.8). The other solutions being mentioned work well but some of them, like FreeRDP or CoRD, are quite technical to set up and use.
More details about each solution, their pros and cons, can be found in this detailed comparison: Free Tools for Making Remote Connections from Macs to Windows PCs.