Whitelisting is for Turbos only at the moment. Connect to to mc.videogamesawesome.com - please read and follow the server rules and keep an eye on the Minecraft forums too! Also, please do not request whitelisting on this page, instead, if you're a Turbo club member, go here.
For TF2 (Turbo only!):
Connect to pastime.ffsit.net (password is ttturbo). The server is alltalk.
Important: If you can't get into the TF2 server because you're not whitelisted, please check that your profile here has a link to your Steam profile in the Steam field. There's also a delay for getting whitelisted on TF2 but it shouldn't take more than an hour after accepting the invite.
For Kill Fun Yeah (Free for all!):
Join KFY AWESOME from the server browser, you don't need a password. Please check this thread in the forums for details.
We've got official and community-run groups for a lot of other games, some open to all and some Turbo only. Here's our GTAV TURBO crew for example. Check out the Video Gaming and Turbo forum to find them. Please do keep in mind that those groups aren't necessarily relevant to the shows in any way ;)