Comcast.com and AT&T is going to start charging extra for Downloading of files,packages, video.
Is there a App for Linux that will keep count of Downloads(Gbytes), like on a monthly basis, so one can keep track of size of downloads for a given month ??

Save yourself the trouble and just switch ISP's. But to only track the usage of files or downloads, not regular browsing would be near impossible. Why not keep a record of everything you download into one directory that checks the total usage?

All the ISPs are going that way so changing isn't going to help.
If there is a angle for them to make more money, their going to.

Our city gave Comcast an exclusive license, and won't permit any other ISP to compete. (Incidentally, the town is essentially run by Harvard University.) So switching isn't even possible.
Apparently aggregate bandwidth consumption is the only thing they monitor routinely. It seems content neutral, i.e., no distinction between, e.g., file download or browsing.

As they keep track, it would seem only right to let me read my counter. But I called, and there's no way for me to see how much I'm using. I'll only notice when they decide it's excessive.

I don't think it's an angle for them to make more money. It's not like an overage charge when you use more than your minutes on the cell phone. Rather they contact you to warn you, and when it happens again within 6 months, they shut you off. (Maybe an indirect angle because you may then be compelled to sign up for commercial internet.)

The tool for monitoring bandwith usage is Tobias Oetiker's MRTG (multi router traffic grapher). I know many big sites use it. However, I haven't deployed it myself.

/Quigi

This seems to be a fast way of getting rid of customers, that most likely won't upgrade to their super duper plan, they will go to another company if they get shut off.

We've had limited plans and (throttling) for-ever in Australia (as well as some unlimited plans). Welcome to the real world. FWIW my ISP has a webpage that shows my usage - current as of midnight last night. Gets reset at the end of each (monthly) billing cycle.
Maybe your lot will provide something similar.

For global statistics about bandwidth usage some people use vnstats. I don't have much experience with it but you might want to check it.