You can certainly use W3TC and hook it in to Varnish to flush, but it's complex and for the vast majority of people, something they don't needs.
Tearstone: I can tell you're still using bad behavior on the gaming site. I can see it in your wp-content folder right now, and when I run a check command, it shows as running and active on that site. If that isn't the domain you want me to check on, let me know. You have a lot of plugins on a highly dynamic site, which runs for logged in users. That means you're just not going to get the benefits of Varnish as much as other people, so ... in YOUR case, W3TC might be a better call.
StephanieVega: Most of the time it IS a theme or plugin doing things in a funky way that doesn't play nice with Varnish. On your site, you've got adrotate, which their developer says does not play well with Varnish. So that's going to be a large part of your problem