you have a password lol, if its WEP, you can d/l a program and in like 5-7 mins somebody is stealing your internets!
to check what you have you need to login to the router most likely 192.168.1.1
WPA2 as far as I know is unbreakable, I say change the key and dont tell your buddies, see if the spikes go away =)
It could also just be a crappy to start with and have a few people on it is not going to help. run a speedtest and see what it runs at www.speedtest.net
if you are spiking a ping that high for 20 seconds or so it sounds like someone is using the conn, if they wer downloading files it would be that way until the download was complete and then slowly go back down. I would think someone is using the conn at the same time causing these spikes.