When I try attaching the cord, whether it be the one that came with the Fire or the Kindle Keyboard, I have a hard time with it. To the point that I'm probably going to break the connection on the Kindle itself pretty soon, maybe in a months time.

When I first tried using the Keyboard's cord, I thought maybe it was that it was smaller or whatever, but I struggled with the power adapter one too.

Anyone else having this problem?

nope, sorry

Yes - I have exactly the same experience - with both the power adapter connection and the USB cable - I wonder if a run of units had slight deviations in either the molding of the plastic case or the shape of the metal connector. I have to "jiggle" and retry several times to get a solid connection.
This may be the first test of Amazon's Customer Service support - if people either start breaking the connector or exchanging the units.

It seems like the cable is a tight fit to me as well - I often think maybe I'm putting it in upside down, even when I'm not.

Same..very tight

And mine's a bit loose. It was connecting - it charged and the red light came on, but there's a lot of wiggle that can go on.

Mine works fine, but I do have a few other devices with this same issue. It might be as @poohbear_nc suggested. It could be that the micro-USB ports from a particular supplier are not as compliant as from other suppliers. Whatever the reason, call Amazon CS and get a replacement Fire.

Same for me. I turned it over a couple of times before finally stopping to see which way it was supposed to go. Mildly worried it'll fail at some point.

Same issue here! I was afraid I was going to break something. :(

I'm REALLY glad I'm not the only one then! This seems like a pretty widespread problem, yikes!