Commentary = Very Inspiring?
What's most important is this: Don't fall to tunnel vision. Being a skilled programmer, level editor or artist is important; but what's going to set you apart from the rest is scope. Read a lot of books, watch a lot of movies, and play a lot of games. Watch movies you wouldn't normally watch, absorb some slightly unusual knowledge. Learn how to write a good short story or play a musical instrument, or how to cook (a hobby of mine, by the way). You pick up little nuggets of brilliance from all over the place, and, as I said, that's what's really going to set you apart.
... of course, if no one understands the ideas you have in your head, it's not going to matter, so learn how to communicate your ideas, too. It helps to have friends you can strongarm into listening to your ideas and comment on them; and come up with a lot of ideas. Not just for game design elements or level design, but for everything you can think of. I think I've learned more thinking about screenplays and collectible card games than I have thinking about 3D games. It also helps to have friends who are intensely critical of everything you do. You have to be prepared to kill your darlings and start over.
Oh, and another thing: Keep a notebook with you at all times. I can't even begin to count the number of ideas I've gotten while getting ready for bed, while out walking, or in the shower, and those ideas have a tendency to fade quickly. Jot everything down, even if it doesn't seem very brilliant at the time. You never know what it might lead to.
That's key.
A CS or EE degree will almost certainly serve you better throughout your life than a game/media degree, but if getting into the industry immediately is your overriding concern, a game program will help with contacts and opportunities.
Exceptional merit will eventually be noticed (perhaps not as quickly as you would like, though), and a degree of any sort is not required if you can conclusively demonstrate that you will contribute great value to a company. However, many entry level positions are filled based on people's opinions about potential, and honest assessments from faculty that work with lots of students does carry some weight.
The best advice is "be amazing", but "diligent and experienced" counts for quite a bit.