It depends alot on the color too.
what a crappy first line, but then again its true. so things to consider are the colors used, the final print resolution, athe resolution of the file and the paper used in the for printing.
the offset print uses 4 colors: cyan magenta yellow and black. lets say your line would be 50% black, also known as gray. the printer would be still using only black ink to produce the gray line, but instead of printing it with solid color (black) the illusion of gray will be produced through a halftone pattern... you know those dots you see when you study a magazine print with a magnifying glass. what it means is that if your lines are 100% cyan, magenta, yellow or black you can go thinner than if the colors are tints. also if your color for the lines are mixed from two color components, lets say you want the firetruck red and you put in 100% magenta and 80% yellow, Instead of getting one fire truck red line, you might end up with two lines that are really close to each other but not quite overlapping, one being 100% magenta and the other one pale, rasterized yellow. This happens because sometimes the paper moves during the printing process or it hasnt been calibrated carefully enough.
... agh, this might be a long post if I try to explain it all... Lets try a short cut:
if you want to use thin lines dont go bellow 0.25pt. and thats if your lines are solid, one component CMYK color.
For tints and mixed colors I wouldn't go bellow 0.4pt.