In my experience, IBM and Toshiba make the most reliable trouble free ones.
A good way of seeing how reliable some model might be is to search google groups (the USENET archives) for message pertaining to the model you’re interested in.
I agree with Pookie on the IBM but disagree on the Toshiba. I work in the business, and my company sells and services all three brands. In my opinion IBM is the most reliable of the three, followed closely by HP (Compaq). I’ve got shelves of Toshibas waiting to be repaired, but very few IBM’s or HP’s. Keep in mind that IBM recently sold their PC business to a Chinese company (Lenovo), so no one really knows how that is going to affect future sales or service.