AMD - Giving Intel a run for their money. They are the leaders in integer math, but with the 3D revolution you need floating point. D'oh! The new Athlon K7 looks like it could take down the Pentium III. If you have the money, the Athlon K7 is the way to go.
Cyrix- Bye bye. Let this be a lesson. Put the megahertz on the chip, not some weird rating. Despite their poor reputation, they were the performance leader. Their 133 MHz chip could outperform Intel or AMD's 133 MHz chip, except they tried to deceive the public, essentially. They marked their chips with a PR rating, like PR166 or PR200... for a chip that doesn't run at that speed and doesn't outperform the competitors chips that run at that speed. Stupid. Really stupid. They had stability and compatibility issues, too.

Intel - The Pentium II was initially released with 66 MHz bus speed, then followed with Pentium IIs that ran at 100 MHz bus speed. AMD was taking a large part of the affordable CPU market, since the Pentium II was such an expensive part. To remedy this, Intel released the Celeron processor. The original Celerons were not well received. They had no L2 cache, and ran at 66 MHz bus speed. So, playing catch-up again, they released the new Celerons, the Mendocino-core 300A and 333, still at 66 MHz bus, but with 128k L2 cache. Although considerably less L2 cache than the Pentium II, the L2 cache in the Mendocino Celerons ran at the full speed of the CPU core because the L2 cache was on the same piece of silicon. Although the Pentium II L2 cache was of much higher capacity, it ran at half the bus speed. As it turns out, the speed of the L2 cache had a lot to do with performance. Then someone figured out that, although the multiplier for the Celeron was locked, all you had to do to unlock the bus speed setting for a slot one CPU was to block one contact on the edge connector. So, the 300A normally ran at 300 MHz, 66 X 4.5, but many users were getting it up to 450 MHz! Then Abit and Asus released motherboards that could do this trick without physically blocking that contact, and allowed users to chamge all manner of CPU settings in the BIOS, without ever having to touch a jumper. With each core revision the overclocks became more stable. More and more users were getting the 333 to run at 500 MHz. Some 300A owners got theirs to 504 MHz. The Celeron was rapidly becoming the overclockers' dream chip. The Celeron 400 made for very easy overclocks, having already been tested at a high clock speed in the first place, and making nice steps with each bus speed setting. 75 MHz bus makes it a 450 MHz CPU. 83 MHz bus makes it a 500 MHz CPU.
    Then comes the Pentium III. The new streaming feature, when supported by a graphics card, can supposedly increase 3D performance by a whopping 30%... unfortunately, the new internal identification code in the Pentium III triggers 30% more paranoid reactions. It's a whole new issue to be debated. I won't take a stance on it right now. I think a bigger issue with the Pentium III would be that it costs more than an AMD K7 Athlon that outperforms it.

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This is really the area where Tom's site got famous, so I'll refer you to some of his most interesting articles on CPUs.

Athlon Kicks the Crap Out of Pentium III?!

Athlon VS. Pentium III Office Benchmarks
Athlon VS. Pentium III 3D Game Benchmarks
Athlon VS. Pentium III 3D Application Benchmarks

Intel Celeron CPU offers great performance via overclocking

(You don't always get what you pay for.)

Remember that Intel Celeron processors are highly likely to overclock to over 400 MHz. The Celeron 400 is virtually guaranteed to overclock to 450 MHz, and likely to reach 500 MHz.
 

Intel	Pentium MMX	233 MHz	$30
Intel	Pentium II	300 MHz	$130
Intel	Pentium II Celeron 300A  Slot One	300 MHz	$70
Intel	Pentium II Celeron 300A  PPGA	300 MHz	$55
AMD	K6-2	300 MHz	$30
Intel	Pentium II	333 MHz	$175
Intel	Pentium II Celeron  Slot One	333 MHz	$65
Intel	Pentium II Celeron  PPGA	333 MHz	$45
AMD	K6-2	333 MHz	$30
Intel	Pentium II	400 MHz	$135
Intel	Pentium II Celeron  Slot One	400 MHz	$85
Intel	Pentium II Celeron PPGA	400 MHz	$50
AMD	K6-2	400 MHz	$40
AMD	K6-3	400 MHz	$100
Intel	Pentium II	450 MHz	$165
Intel	Pentium III	450 MHz	$175
AMD	K6-2	450 MHz	$50
AMD	K6-3	450 MHz	$140
Intel	Pentium II Celeron PPGA	500 MHz	$135
Intel	Pentium III	500 MHz	$230
AMD	K7 Athlon	500 MHz	$220
Intel	Pentium III	550 MHz	$375
AMD	K7 Athlon	550 MHz	$340
Intel	Pentium III	600 MHz	$585
Intel	Pentium III 600B	600 MHz	$650
AMD	K7 Athlon	600 MHz	$500
AMD	K7 Athlon	650 MHz	$680