My AMD 386 clone was a complete turd, but that doesn't say much about today's products. I'm still using an AMD Athlon 64 4000+, and my nVidia 8800 GTS 512 picks up most of the slack.
If you want stability, go with an Intel Core 2 Duo or Quad and an Intel boxed motherboard. Intel's boards don't have legacy connectors--parallel ATA, PS/2, floppy, etc.--or even PCI slots in some cases, so keep that in mind. i.e. If you want to a use a Catweasel, go with another brand. I like Asus.
Buy memory tested and approved by the motherboard manufacturer. If you're running a 32-bit operating system (not just Windows), don't install more than 3 GB or so of RAM, depending on how your motherboard maps your add-in cards and onboard widgets into the 4 GB address space. If you're running a 64-bit operating system, don't worry about it, and buy as much memory as you can afford. I'm still using 1 GB but could probably benefit from upgrading to 2 GB.
Buy a hard disk based on cost and warranty. (My rule of thumb: buy the disk just below the point at which the cost increases at a higher rate than the capacity. Seagate's 1TB "SATA-II" disks are reasonably priced, and they have a 5 year warranty.)
Buy a SATA optical drive that meets your needs. DVD+/-RW DL at minimum, Blu-Ray if you can swing the added cost now.
Buy a media-friendly graphics card--any of the midrange nVidia and ATI cards should do; however, nVidia is doing wonderful things with CUDA, PhysX, and general purpose programming on their GPUs, i.e. not just for gaming. The midrange cards typically have hardware-assisted Blu-Ray/HD-DVD decoding while some of the high-end cards do not. Do a bit of research before buying.
If you plan on watching high-definition video content, make sure your monitor supports HDCP over DVI or HDMI (or use something like AnyDVD HD--an awesome and easy to use program--to disable HDCP completely).