It depends on the type of router in use.
If the owner has a packet sniffing program running, they could read all of the non-encrypted information and probably figure out who was on their network by reading enough of the information that goes by. They wouldn't need to be home for the packet sniffing program to be running. They could just leave it running all the time and have the information saved to disk for inspection later.
Most routers will keep a list of all DHCP leases currently in effect. If the lease time is set to be weeks or longer, then there is a list of all MAC addresses currently with a lease. Some routers even can associate the host name of the MAC address and keep that in the list. So, in the case of your ipod touch, if you named it "Bubba's iTouch", then that name will be in the list. If your name is Bubba, then it would be super easy for your neighbor to figure out that 'hey, bubba from next door has been using our wifi'
The reality of the situation is that most likely since your neighbor is so lazy that they did not read the directions that came with the router to set up security that they are totally clueless. So clueless that they will probably never realize that someone else is on their network as long as the people using it don't hog the connection or do anything illegal.
If someone were to start downloading torrents over their connection, the owner would quickly realize that something was going on since their download speeds would be horribly slow. Also, if the police show up on their doorstep and haul the owner away for committing an online crime that they didn't commit, they might soon realize that someone else was using their wireless network.
So, my guess is that as long as you don't abuse the connection, the chances of getting caught are pretty small.