I was just recently dealing with this-- of course, I am sort of limited to what I can get locally just so I don't have a 4 week turn around to get it repaired if there is a problem.
Still, HP and Lenovo have the best customer service in the industry. Asus has the fewest hardware failures of any PC manufacturer.
That said, I have a 5-year old Dell that has been through 3 years of 4 users (in my family we have the adopt-Elly's-PC program-- and 2 of the users have dropped it multiple times, amongst other things) the only problems are a few dead pixels on the bottom of the screen and the battery should really be replaced. On the other hand, it was a custom-built business PC and a bit sturdier than the consumer models.
I had a gateway for a few years. I never had a problem with it, but it just wasn't durable in the long run and the motherboard died after a little over 3 years.
We also have a Toshiba (one of the newer "entertainment" versions) that has made it a year in a very rough and dirty environment with no problems so far.
Of course, there is Mac which has a great following on its own, but if you are a PC person it is a pain in the butt to learn a new system (or maybe that is just me and my dying brain cells). People rave about them, but my only experience with the laptops has been trying to deal with the problems that crop up with a generation of older mac books that are underpowered for what they are being used for. I haven' t been impressed by the durability so far. As they have aged the actual shells have yellowed and cracked in our harsh, dry climate-- which leads to other problems.