Every company I've applied for only requested either a portfolio website link, or 3 images of my work, so I have never sent a printed resume. I have used the resume on my website, and my initial email as a cover letter.
What I write depends on the company. I try to mention an ability to produce assets for games they have made in the past, or a project that I know they are currently working on. It's mostly mentioning my abilities, the school I recently graduated from, and thanking them for taking the time to look at my portfolio.
I have applied for 12 companies in my area. One company immediately replied the second I sent my application with an automated email saying they had my portfolio on file, and would contact me if interested. Another company got back to me after a few months with another automated email saying they weren't interested in me at this time. None of the other 10 companies have contacted me.