And wouldn't you know it, there's already an app for that. Developed by the same guy who made ShootMe, PicMe (free) allows root users to view and even control the EVO by visiting a custom IP address (provided when you launch the app) on a remote web browser. Just right-click the image on your computer to save/capture the displayed screen in PNG format, and refresh the page to update it to whatever is currently shown on the EVO.
There's also a live mode for two-way control (i.e., you can interact with the EVO or the computer) that can be viewed in a Java-based standalone player or in the browser. This feature was added in an update (the current version is 0.7.5) and still needs some work in its implementation, but if you're an old Windows Mobile user and have been searching in vain for something similar to Pocket Controller Pro, then PicMe is probably your best option right now. I just use it for its originally intended function (screenshots), but the live mode would be useful for demonstrating something remotely, doing videos without your hands/fingers getting in the way of the camera, and maybe making others think your EVO is possessed.
You can get PicMe for your EVO from this direct Market link or by scanning the QR code below.