Sid,
I don't know about animation and the like, but for programming, complete means either a running demo, or an app which shows the usefulness of a full-fledged algorithm/concept.
Jeku,
The problem is, with the Games Industry booming, every man and his dog that's got a programming degree is after the same job as you.
If you can show to them that you've got the skills (and at the same time pass their aptitude test), then you're head and shoulders above the rest.
For example, I'm completing a Thesis for my final Honours year this year at Uni. I could have optionally gone for industry experience.
We had a number of companies come to our Uni to try and recruit people for the industry experience, so I went in to get some interview practice. They basically threw themselves at me after I showed them what I'd finished. Compared to the other students who had exactly the same level education, and one other who is about the same skill level as me (we were top of the class), I was the one they wanted.
It's all relative, though.
If you go into an interview, give a good aptitude test and leave a great impression on the intervewer, you're more likely to get the job again.
My recommendation still stands to any and all that a good portfolio can put you up above others with the same skill level.
