Thanks to everyone for the help! 
Especially to Brian Sherwood who helped me finally figure it out. I didn't "set terminal png" because I didn't have a terminal connected to the Solaris box and wasn't using X. However, this needs to be set anyway. Also, "set output graph.png" needs to go *before* the plot statement.
The data I mentioned earlier is in /export/home/router/erx-cpu-util/36w/util.txt
Here is the very brief gnuplot program that now works:
-bash-3.00$ cat graph-36w-cpu.plt
#!/usr/local/bin/gnuplot
set terminal gif
set ylabel "Percent CPU Utilization"
set xlabel "time"
set output '/export/home/router/erx-cpu-util/gnuplot/36w-cpu-util.gif'
plot '/export/home/router/erx-cpu-util/36w/util.txt' using 1:2 title "card1" smooth csplines, '/export/home/router/erx-cpu-util/36w/util.txt' using 1:3 title "card1" smooth csplines
Thanks again,
scott