The driver in the haiku repository has a known bug… the transfer just stops while performing an ftp transfer ( ftp, wget) or loading a web page ( NetPositive, Opera.) To get some use out of networking use these two commands in rapid sequence from a Terminal:
ifconfig /dev/net/rtl8139/0 down
ifconfig /dev/net/rtl8139/0 up
This will make the transfer continue again.
If you have downloaded BeOS MAX, copy /boot/beos/system/add-ons/kernel/drivers/bin/rtl8139 to the same location on your Haiku install. This driver seems to be working correctly without the hang problem.