College does matter for your first job. Seriously it does. Forget the IITs and the NITs. You'll always manage to get a good job there in campus placements. If you get into those, good for you. End that debate here.
Let's talk about the private colleges since no one has thrown the perspective on that.
I'll just point out some live examples -
1. My college, which is one of the known private colleges in Pune, had the worst possible T&P dept. We had 3 I.T. companies for our entire batch and the T&P ma'am tells me "we already have 3, what else do you want?" when I ask here will we have more companies coming in.. :|My friend's college on the other hand had a fantastic T&P dept. They got the entire batch placed by the year's end. I was lucky enough to get into a medium sized company(off campus) where I'm getting fantastic exposure.
2. My friend's elder brother did his engineering in I.T. from a small college which had just completed 2-3 years and was yet to have it's first T&P. However, luckily he managed to get into Sapient (through campus placement itself) and after 9 years (no masters degree) and one job switch later, he is now earning a 6 figures salary in the U.S.
The point I'm trying to make is that for the first job, the college name and brand does matter. You get a good starting package, a good company and if you put in some efforts, you can steadily rise to the top.
After 5 odd years, no one is really going to care. What I've seen is that after every educational milestone, i.e. school, then college, then the first job, the last one starts seeming more and more insignificant. Of course there are companies who only shortlist on basis of IITs and IIMs even if the person has years of experience, but most of the companies don't.
Later, the only thing that matters is what company you have worked in. I feel that branding helps more in the later stages of your career.