UTF-8 Reduce Ascii art
GolfScript (90 chars)

n/.,1&amp;[""]*+.{,}%$-1=.1&amp;+{1$,-´' '*+}+%2/{zip 2/{~+0\{32=!1$++}/" ▗▝▐▖▄▞▟▘▚▀▜▌▙▛█"3/=}%n}%


A lot of this goes to handling ragged arrays. Nasty test case:

xx
xxx
xxx
xx
x


contains a 3 different 2x2 grids with only one of the 4 cells containing any character at all.

To make things worse, the zip transposition to chop the columns into pairs gives the same output for ["xx" "xxx"]zip and ["xxx" "xx"]zip. I therefore begin by padding out to ensure that all lines are the same even length, and that there are an even number of lines. 

Note that this program assumes that the interpreter will treat " ▗▖▄▝▐▞▟▘▚▌▙▀▜▛█" as a string of length 48, even though as per instructions in the question I'm counting it as 16 chars plus delimiters.

I've tested this to the best of my ability, but I can't find a monospace font which actually renders those characters correctly.