My friend had a great launch failure with one of those. He had a two stage rocket with a payload section, but got the stages backwards. Also, in the payload section, lacking any handy bugs, he put some gravel in (not sure why). So, the thing went up, but because the stages were backwards, it didn't fire the second stage immediately. This gave the rocket time to spin a bit: the gravel held the nose down and the tail flipped up. At that point the second engine kicked in, and the thing shot straight at the ground and smashed to bits. It was pretty cool to watch.
The further away the center of mass of a rocket is from center of pressure the more stable the rocket is.
Apollo's Launch Escape Vehicle, which was essentially a rocket with the payload below the engine, had a few hundred kilos of depleted uranium ballast placed at the top exactly for this reason—to move CM far enough for the vehicle to be stable.
Interesting, but it wasn't for that reason: those things are designed to be (and mostly are) stable without putting a bunch of weight on one end like that.
Not sure what you mean by "those" things. In LES case the reason was the one I stated for a simple reason: LES did not have gimbaled engines and had to rely on aerodynamics to be stable. Launch Abort System for the new Orion spacecraft will have attitude control motor and thus no need for ballast. See http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/2008001... for more. I will quote just a bit:
Another key difference from the Apollo launch escape system is with regard to control. Apollo utilized a passive system that relied on ~1,000 lbm of ballast to keep the abort vehicle passively stable during the escape rocket burn<…>
