I have owned two Gateways and one Dell. The Gateways were both far superior in their overall build quality and reliability.
My first Gateway developed some "random-restart" issues two weeks before the end of the extended warrenty....they replaced the motherboard and power supply, but neither of these made any difference, so they just gave me a new machine, no hassels. Not only was it a new machine, but a far superior one at that....in return for a 266Mhz Pentium 2 I got a 733Mhz Pentium 3, etc. That was three years ago, and this machine has been upgraded to death and is still going strong (I'm using it to type this post).
By comparison, my parents got a Dell Demision 4100 about 3 years ago.....fans were horribly noisey out of the box (Dell said it was normal....yeah right!).....the CDRW just died a couple of weeks ago; looks like a dead laser......it has already burned out two RAM modules (one pre-installed, one bought later FROM DELL), but Dell would not replace either of them! I am not joking or embellishing this at all: when I called about the second chip (after replacing the first with Crucial RAM), the tech told me to re-install windows!!! (Appearantly you need to be running the original OS for Dell to provide tech support) The computer would not run for more than 5 minutes withut crashing with memory errors, yet he expected it to last long enough to do a two hour install of the OS.....
So, basically, if you want the advice of a very seasoned Windows user who has helped many friends and family buy and then (attempt) the keep their PCs running (soo many lost days.....agony.....), avoid anything from Dell and Compaq*. Anything from Gateway, HP, and IBM should be reasonably good (by PC standards).
*Now that Compaq has been incorperated into HP, I assume that they are just HPs with different cases, so in theory I suppose they should be better...