Although you don't show data, but I can assume that you just have n-datapoints for a n-polygon.
There is no reason why gnuplot should automatically close the curve to a polygon when plotting with lines or with linespoints. This would mean: adding the first datapoint again at the end.
You have to do this yourself.
You can do this via external tools like in Miguel's solution.
You can also do it with gnuplot only which would be platform-independent. Basically, you store the first and the last data point in x0,y0 and x1,y1, respectively and plot a closing line with vectors.
Data: SO32954260.dat
0 0
1 1
2 1
2 0
Script: (works with gnuplot>=4.4.0, March 2010)
### plot closed polygon
reset
FILE = "SO32954260.dat"
set offsets 1,1,1,1
set key noautotitle
set style line 1 lc rgb '#ff0000' lt 1 lw 2 pt 7 pi -1 ps 1
plot FILE u ($0==0?(x0=$1,y0=$2):0,x1=$1):(y1=$2) w lp ls 1, \
'+' u (x0):(y0):(x1-x0):(y1-y0) every ::::0 w vec nohead ls 1
### end of script
Result:
