Degree hardly matters. Our department advises us to list the 'education' section of our resume
at the very bottom. Employers want to know your skills; they want to know what you are good for and whether they could put you to use. Skills go at the top; where you got them doesn't matter. It's a plus to see a degree, as it shows you have your head screwed on straight enough to at least stick with long-term goals, rather than wandering off.
Quite frankly, the real value of a degree is industry contacts. Coming out of RIT, I graduated with people who work at Microsoft, Sledgehammer Games, Zynga, and a variety of other big name companies; along with dozens of small ones. As a direct result of those contacts, I've had interviews with all three of those. Then there's faculty. My first internship was handed to me, literally without a technical interview, simply on the word of a professor. I've had another several interviews for internships through similar industry contacts. As one student was talking about, a professor made a comment on facebook, and suddenly he watched in amazement as several big names in the industry responded; pretty much a full list of his childhood game designer icons. As he put it, it was like walking down the street, looking down an alleyway, and seeing a meeting of The Justice League. That said, RIT does much better than most universities in career services. We have a 3/4 year work experience requirement to graduate, so the university is financially invested in helping us find jobs (poor graduation rate = low rankings = less revenue).
Now to build on what was said before: Portfolios. Our major, Game Development, all but requires them. You may not think them all that relevant, but let me guarantee you this: Employers do. If you do any sort of graphics programming, UI, ect, it is absolutely required if you want to be hired. For non-graphical work, make one anyway. If an employer gets 2 resumes of about equal quality, and one has a URL for a portfolio website with detailed descriptions of what they've done in the past and their role in projects, that resume is instantly more valuable. Make sure it's well designed and engaging, showcasing your expertise and areas of interest without time-wasting, overly adjective-ridden, redundant, and simply hard to read fluff distractions. Make it shiny, because HR people are even less willing to spend time on your web page than most people.
Some portfolio examples:
http://mculek.blogspot.com/ <--- guy who, last I heard, worked on MS's DirectX team
http://people.rit.edu/jja2535/ <--- some random dude
When it comes down to it, a resume alone simply can not stand up to those without outclassing them entirely through experience. A lot of employers won't look at them immediately; as early stages of hiring are often up to HR people, but for the latter stages, make sure you point them to your portfolio; particularly when they ask for details about projects mentioned on the resume. Explain the details, but also let them know there are more details and such on the portfolio website if they want detailed info about a variety of projects.
As for a resume, skills at the top, work experience or projects next (order of these 2 depends on which is more relevant/impressive), education at the bottom.
Another thing which can help a lot is going to professional conferences. For graphics programming, that means SIGGRAPH. For game development, it's GDC. Just be sure to treat people there like
people and like colleagues. Begging someone for a job just annoys/pisses them off; asking about their work and the technologies and such they work on will get you contacts/friends in the industry who you can later follow up on for job leads; either for their company or those they know of. Find conferences like those, and if you can, go to them.