I've had an Asus laptop for 3 years and it has been on for weeks at a time (not sleep mode... but actually ON and running). I also had the screen crack in my bag and a hard drive failure at one point and ASUS's warranty and customer service was actually really good on timing and service. It was honestly the least hastle I've ever had getting a piece of tech re-worked by a major company (well.. tied with my RROD'd 360).
I'd recommend ASUS for sure and tell you to stay away from Acer, Dell, HP, MSI and Toshiba. I'd also recommend Lenovo. Although the Thinkpad brand has diluted since moving from IBM to Lenovo, they're still very well spec'd machines with excellent damage prevention measures and great design (well.. I'm a really vanilla guy so I like the design) for reasonable prices.