Back in the day I used to do a lot of streaming and recording. Many times I would plug in a PS2 or a Gamecube and record from there.
This little doohickey here is the AverMedia Live Gamer HD 2. It can record games in a standard 1080p 60fps and takes video through HDMI.
In the past, I used to use a USB version of this called the Live Gamer Portable. My PCIe slot was taken up by a WiFi card, so this took up a USB port on my PC. It even supported component with it's own cables! I have never a fan it though- It only worked with its own software that only worked when it felt like it. This PCIe capture card changed the game.
This will need an overhaul when I get back into streaming...