Typically, drywall sheets hung horizontally are hung with the upper full sheet first against the ceiling, cut bottom sheet last. This is so you will have an indent at the top to tape and mud. Unless your wall is exactly 8 feet tall, the cut of the bottom sheet is at the floor, thus no indent. Even if you have an indent at the very bottom against the floor, it is only about 2 inches wide. Common baseboard is 3 1/2 to 4 1/2 inches wide and will bridge this indent and is nailed mid and high. We have never put mud on the very bottom of a sheet, even it the indent is there. I suppose if your baseboard is very narrow, you may have to ask the mudders to fill that area, but that is very uncommon and would be a special request.
I've encountered the same problem in my own home, although the drywall and ceiling seam cracks only showed up one at a time over the course of a few years, and most of them were present when I moved in. If more than one or two seams popped or nail heads started showing within a month, that seems like it could be a rather large settlement in your foundation, or some other structural problem.
I'd highly recommend getting a foundation specialist to your house sooner rather than later to see if your foundation might need piers to support part of it, or if some other repair is required. In my house, a total of 14 piers were needed along the side and front of the house to support one side and prevent further shifting. There were a few hairline cracks (even small cracks can be a bad sign depending on where and how many they are) in the foundation walls, and the corner of the house had settled over 2" before the problem was found.
The problem could also be in load-bearing structures (walls, I-beams in the basement, etc.), especially if it seems the problems are mostly towards the middle of the house.
The sooner you get this fixed (don't just let it go, even if you have to pay a few thousand), the better. You'll avoid more drywall repair later, and prevent further settlement and degradation of your house's structural integrity.
Best Answer
It looks as though one or both sides have not been adequately fastened to a framing member or "nailer" (nailer being a wood board that is not a framing member but instead was placed specifically to facilitate the fastening of the wallboard).
You could check by gently pushing against each side along the cracked corner. If you push back and the wallboard stops up against something solid then you may have something to nail/screw to; if not then it was improperly installed without something to nail/screw to.
Tape and mud alone will not work because the wallboard will continue to move and will crack again at that spot.
The best repair option (some may say the only option) is to cut back to the next stud and remove the wallboard, allowing you to install a nailer. Then replace the wallboard and mud/sand/mud/sand ad nauseum...
I had the same situation in my own home, as an experiment I installed 4 small steel corner braces along the crack. I traced their footprint and cut and scraped the wallboard so they sat almost flush, using short drywall screws to anchor them; this held the two panels together at the corner. Then I mudded over them and sanded and primed and painted and it still looks good today (3 years later), no further cracking. This is definitely not the preferred repair method but hey, it might be worth a try if you don't want to tear out the walls.