It seems to mostly happen on the .1" grid IDC header type pins. I have some Molex connectors (single row .1" grid) and some larger screw-terminal connectors that do not get the icicles. But, the two-row .1" grid headers are the ones that seem to capture a big glob of solder, probably on the lowest rows of pins, as I tilt it out of the solder pot.
So, it is not some specific part number, but a very generic type.
Jon