I like pens and the boarding card usually gets a fine blue-black ballpoint. Somewhere around a 0.4-0.5 mm so the immigration or customers officers can read it from a distance if their eyesight isn't so great. Or would be able to if my handwriting was better than chicken scratch.

As clockmilk mentioned, pen forums do have this type of question. Fountain and gel inks can smear in water, say disembarking via remote gate and it is raining outside, though water resistant and water proof formulas are available. I tend not to bring those when I travel because the last thing I want to worry about are stains from an improperly pressurized pen filled with water proof ink leaking onto my non-synthetic clothing.