Whilst I realise that this kind of thread is often open to "mine is bigger/better/shinier than yours" flame wars, I'll chance my neck as follows.
The main reason any electronic kit fails is overheating (as this either burns out components directly, or results in thermal expansion that causes weak circuit boards/tracks or solder joints to break). Open up any desktop system and you'll see its mostly a box of air with lots of fans to circulate said air past the components that need cooling. Clearly a laptop doesn't have this luxury. Therefore manufacturers have 3 options:
1) slap in loads of heatsinks/cooling fans and vanes and get heat out somehow
2) increase build cost by using components that are more heat tolerant
3) say F*ckit, use cheapy components and accept that most units will fall over and die 3 days out of warranty.
Clearly options 1) and 2) add to cost, whereas 3) is a budget option. If you want a workhorse laptop that will last a reasonable length of time you are probably going to have to pay a bit more for it. If you buy cheap as chips then expect it to last as long as a bag of chips.
IMVHO (and all based on personal experience) I wouldn't touch a Toshiba again (3 motherboards in 13 months
) Sony Vaio range seem very well built and seem to last - I'd recommend to anyone. That said I do know of one colleague that has had real issues with his Vaio. Dells seem OK ish (although the cheaper offerings don't really last well). Similarly Compaq
One other point though is to look at what you want from a laptop. If you only really want a very lightweight (both physically and in terms of performance) machine for reading emails on the go and typing a few documents, some of the ultrasmall netbooks use very little electrical power and thus stay very cool. I currently have a Samsung NC10 and this often gives me 8 hrs battery life. Can't complain.
Just my £0.02, Hope this helps