VNC, or Virtual Network Computing, isn't itself a product, but an open-source remote-control and display technology that's implemented by Tight VNC (free), Ultra VNC (free) and RealVNC (free and pay), among other parties. VNC isn't hard to use, but it's not as simple as Join.me and TeamViewer, which don't require user knowledge of IP addresses.
To use VNC, install it on both the PCs you want to connect and then set them to listening. To control another PC, simply open the VNC viewer (client), enter the PC's IP address, and have at it. You may also have to open port 5900 on your firewall and router, and to direct said port to the PC you want to control.
You can use VNC to connect to multiple PCs behind a public IP by opening and using more ports. Most VNC implementations install both the server and viewer software by default, so (as with TeamViewer) you can control in either direction.
Though it's a tad difficult to set up, VNC is cross-platform (Windows, Mac, Linux), and it works extremely well once installed.
Join.me is a meeting service (free and pay) from LogMeIn that also provides remote control. It's convenient for impromptu support in that all you need on the controlling PC is a Web browser. The user with the computer that will host the meeting (and offer control) simply surfs to the Join.me site, selects Start Meeting, and downloads a file.
After running said file, the meeting originator passes the provided nine-digit passcode to the user or users on the other end, who in turn enter the passcode in the Join Meeting field on the Join.me homepage. The meeting originator's desktop will appear in the browser. Once remote control is granted, you can chat, send files, and more. Easy-peasy, but note that Join.me isn't suited for unattended remote control, which makes it only a partial replacement for LogMeIn.
Most users think of WebEx as a tool for multiuser boardroom meetings, but it's also perfectly suitable for small-scale, live (not unattended) remote control and support. WebEx works a little differently from Join.me in that installing software is required at both ends, but that's a relatively painless procedure.
Once users have joined the meeting, initially they can only view the originator's desktop, but the originator can make another person the presenter, pass control over the mouse and keyboard, and share files, chat, and utilize webcams for face-to-face interaction. There's a bit of a learning curve if you stray from the main features (available from the usual drop-down panel at the top of the display), but overall WebEx is quite easy to use.
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