Are you downloading/uploading ANYTHING while playing?
Are you using Wireless or is your connection wired?
Are you sharing internet with anyone? I.e., college, apartment, etc.
I used to get bad lag spikes (I dont play anymore). It's mostly because Jagex's servers are outdated. My computer can handle WoW with no lag, but I lagged playing RS.
I was getting lag spikes at the same time as someone who was helping me do DT today. It made me die once when I was killing Kamil . I use a brand new computer quad core with 8gb RAM and Comcast Highspeed Internet. I doubt it was my connection.