From Wikipedia
"New class action lawsuits have been submitted December 2006.[4] One discussion forum, guessing that some of the iBook problem was caused by the GPU losing contact, found that placing a shim between the plastic casing and the GPU solved the problem—and that Apple was using this solution also (the video can actually even be reactivated temporarily by squeezing the machine midway between the trackpad and the left of case). For a detailed explanation of the technique for iBook G4 models, see this guide; for the iBook G3, see this guide.
On May 2, 2007, the Danish Consumer Board published an extensive report[5] made by an external party concerning the Apple iBook G4 logic board issue. Also a press release[6] was made, referring to the global consequences this might or will have for possible guarantee claims.
The pre-1 GHz G4 models also suffered from the dead video problem, however it was not caused by the GPU separating from the motherboard, but rather a sub-processor chip found on the underside of the iBook G4, that separates after usage (heat expansion and contraction)."
Looks like if you find an iBook with a CPU Frequency higher than 1.0ghz you're safe.......