If I have a computer with a 2.66GHz quad-core processor, will it run my software and games faster than my 3.2GHz single-core Pentium 4?
Yes, quad-core CPUs are generally much faster than single-core CPUs -- even if the single-core CPU has a faster clock speed. In the modern computing world there is less emphasis on numbers -- MHz and GHz mean relatively little. Instead, we look at the architecture of the CPU to give us a clue as to how fast it is.
A quad-core CPU is actually constructed of four separate processors squashed on to a single chip. In your example, each of these cores runs individually at 2.66GHz but they work together to get the job done quicker than a single-core CPU would. Imagine four Tim Henmans playing simultaneously against a single Roger Federer and you'll start to get the picture. Tim may not be the better player (on paper), but four against one is really no competition.
You may not notice much difference between single-core and dual-core PCs when running simple applications. Dual-core only comes into its own when multitasking -- for example, running several applications at once. If you're the type of person that likes to surf the Web while you listen to music, burn a CD and run antivirus software, multi-core really is the way to go.
Some applications run better on a dual-core PC than others. Those that do support a technology called thread-level parallelism (or TLP). This is where several parts (or threads) of an application run independently of each other. These individual threads can be assigned to each core of a multi-core CPU for better efficiency and speed.
Even if an application isn't multi-threading-enabled, Windows XP and Windows Vista are smart enough to take advantage of multi-core CPUs. They can load one core with one application, and the remaining core(s) with separate apps.
Games are a separate issue. Most are not multi-threading-enabled, so in some cases, games will actually run slower on a multi-core CPU than they would on a single-core chip. This situation is changing, however, and many titles, including F.E.A.R and Doom 3, now take advantage of multi-core. In the future, games will utilise separate cores for things like artificial intelligence computations, graphics rendering and audio, so multi-core is where it's at.
Hope this helps!