The processor you should get depends on the type of computer you want:
For Laptops:Intel Centrino Duo (using Intel Core Duo [32 bit] or Core 2 Duo [64 bit] processors) is the latest of Intel's mobile offerings. It offers low power, dual-core processors (so laptop will run cool), as well as excellent battery life. You should consider these as there are some very affordable deals out there. If you cannot afford these, then the 'original' Centrino (with Pentium M processors) is still an excellent choice, and prices of these notebooks have been falling as this is an outgoing technology. For cheaper Intel laptops there is the Celeron M. Laptops using this will not have as good a battery life as Centrino Laptops. On the AMD side of things there are AMD Turion 64 laptops (performance version), or Mobile Sempron for cheaper laptops.
For Desktops:This depends on what you use your desktop for. If you just use your PC for Microsoft Office / Internet / Email / Listening to Music / DVDs, then any of the latest Intel Celeron D or AMD Sempron processors will be fine for you.
If you multi-task lots - i.e you run lots of background applications, have a lot of windows open at once etc....- then the processor to get is really determined by your budget:
- - Intel 'Netburst' based chips (Pentium 4, Pentium D) - As Intel has released its next generation of high-performance Core 2 Duo chips, these previous generation CPUs can be found reasonably cheaply. The P4s have Hyper-Threading, which makes them good at multi-tasking, and the Pentium D's are dual-core, and are better at multi-tasking than P4s.
Low to Medium Budget:
- - AMD Athlon 64 X2's - AMD has slashed prices on these dual-cores, making them very attractive. The best value chips here are the 3800+/4200+. Also, the lower models of the Core 2 Duo range (E6300/E6400) are also very good value.
Medium to High Budget:
- Any of the higher Core 2 Duo models (E6600/E6700) are amazing performers! Also, you can now get some of the higher models in the Athlon 64 X2 series at modest prices now. If money is no object, then get an Intel Core 2 Extreme. These CPUs are the fastest that money can buy at the moment.
If you use your PC for video editing, then any of the dual core processors mentioned above will be perfect for this!
If you are a PC gamer, any of the single core Athlon 64s will be good -- these are avaliable insanely cheap now, leaving more money to spend on more important components, i.e. graphics card! For those who have to have the best, the Core 2 Duos are excellent gaming CPUs, and they will become even more attractive as their price falls!
One word to mention about PC gaming systems; it dosent really matter what processor you get as long as it is a fast model -- there are much more important determining factors in how fast your game will run: The amount of RAM will be fairly important (get at least 1GB of dual channel), but not as important as the graphics card. A really good graphics card is essential. I wont discuss these here, as that is for another place, but good cards are GeForce 6800GT/Ultra, Radeon X850XT PE , Radeon X1900XTX and GeForce 7800/7900. Also, the more mainstream GeForce 7600GT and Radeon X1800 GTO offer great value. I believe that some X1800GTOs made by Connect3D and HIS can be 'unlocked' from 12 pixel pipes to 16, giving an increase in graphics performance, but I cannot verify this. Google "X1800GTO unlocking" or somthing similar to find out more! For more advice about what are the good graphics cards (and CPUs and virtually everything else to do with PCs) then look at any hardware review sites (E.g. AnandTech, techreport ...)