I watch my characters arm move the axe and the logs filling up my inventory. Nah, not really! I just do whatever I can do, e.g. play psp, go on youtube, listen to music.
Some tips that are helpful when overcoming boredome are;
Listen to music.
Talk on the Phone/AIM/MSN.
Myspace/Facebook.
Watch videos, or browse forums. If you're watching videos, make both of the screens(video/runescape) small enough so they both fit on your desktop.
I usually play Halo3 when i'm fishing/training.