Histogram using gnuplot?

I know how to create a histogram (just use "with boxes") in gnuplot if my .dat file already has properly binned data. Is there a way to take a list of numbers and have gnuplot provide a histogram based on ranges and bin sizes the user provides?

yes, and its quick and simple though very hidden:

binwidth=5
bin(x,width)=width*floor(x/width)

plot 'datafile' using (bin($1,binwidth)):(1.0) smooth freq with boxes

check out help smooth freq to see why the above makes a histogram

to deal with ranges just set the xrange variable.

I have a couple corrections/additions to Born2Smile's very useful answer:

1. Empty bins caused the box for the adjacent bin to incorrectly extend into its space; avoid this using set boxwidth binwidth
2. In Born2Smile's version, bins are rendered as centered on their lower bound. Strictly they ought to extend from the lower bound to the upper bound. This can be corrected by modifying the bin function: bin(x,width)=width*floor(x/width) + width/2.0