AMD vs Intel

Both Intel and AMD offer a wide range of CPUs. The two companies' products are in direct competition and are both capable of running any current PC software. The differences are in technical details that, although they may be used for marketing, don't necessarily mean much to the end user.
Pricing is also very competitive, with AMD's products being generally cheaper than comparable Intel models. At the budget end of the market, Intel's offering is the Celeron which is a cut-down version of the Pentium 4. AMD's budget processor, the Duron, is still available although it's getting harder to find.
In the mainstream desktop market it's Intel's Pentium 4 versus AMD's Athlon XP and Athlon 64. The chief difference between the two is that the Pentium 4 and Athlon XP are 32bit CPUs, while the Athlon 64 is a 64bit model (see later on for an explanation).
Just recently both companies have launched new ranges of processors, Intel with the Extreme Edition of the Pentium 4, an expensive model for the hardcore gaming market, and a new version of the Pentium 4 processor. You might see this referred to as Prescott to differentiate it from the previous Northwood version. The technical differences aren't huge, but the pricing hasn't changed for models at the same clock speed. So if you're given a choice, ask for the Prescott models.
AMD has also introduced the Athlon 64 FX range, a high-end gaming/workstation CPU that prompted Intel to launch the Pentium 4 Extreme Edition.
Other choicesIf you're looking to build a very small system from scratch, then Via's Epia platform is worthy of your attention. This platform consists of tiny (17 x 17cm) motherboards with the Via C3 processor already fitted; you can't upgrade the CPU. At 1.2GHz, the fastest C3 may not be able to match its bigger desktop cousins in performance terms, but it allows you to build low cost, space saving systems.