Asus has quite a good reputation for its laptops, although I have always been very underwhelmed by the lack of quality in its optical drives. Its motherboards are generally pretty good.
However, you should probably buy carefully; Asus laptops crop up frequently in grouptests and can get a great review one month but a very mediocre review the next. And that's from the same reviewers. At least one recent grouptest from a well-respected publication had two Asus models; one was well-liked, the other was very average. It seems to be a less consistent brand than, say, Lenovo, Sony, Acer or HP. I must admit to knowing little about how Asus' reliability measures up against the leaders in that respect as I haven't seen figures for it.