I have owned an Asus screen, several Asus wireless routers (1 router, 1 working as a bridge, 1 when i lived elsewhere and their mini pocket router) and some asus fanless graphics card. All still in use and still working, the routers are 2 to 3 years old, the cards both about 2 years old etc. Oh, and we had the barebones Terminators at work in a past company, no complaints there either.
Could have been lucky in my choices but it does give me some confidence within these range of products - although whether it carries to laptops is anyone's guess since I think most manufacturers actually only assemble. And I still check specs and reviews before I buy anything
Other laptops I have had great experiences with are fujitsu (but know people who didnt, on that one)
My partner has an Asus notebook with an ATI card we snatched on ebay and it's solid
Not sure what notebook I would buy if I bought one now, alas my requiremements tend to go contrary to the market (high res but small screen etc.)