133MHz SDRAM is only a little more expensive than 100MHz SDRAM, and with the sharp falls in memory prices, I don't see any reason not to buy 133MHz RAM. It will work with everything, pretty much. You might even want to buy 166MHz RAM if you can find it, ensuring future upgradability.
(1) Intel Pentium III
If your PIII has a 133MHz bus you will almost certainly need 133MHz memory on a Intel 810 or 815 chipset. If you have a Intel 820 board with an MTH (memory translator hub) then you will need to use 100MHz RAM. The 820MTH boards are not very common anymore though, and are no longer produced.
Some PIIIs still have the 100MHz bus, which will need 100MHz memory. Note that you can always use 133MHz memory running at 100MHz (underclocking). This won't hurt a bit. The inverse is <b>not</b> true - don't overclock 100MHz RAM to 133MHz unless you know what you're doing
A Pentium III with a 133MHz bus has a 'B' after its name, e.g. PIII 800B runs at 133MHz FSB, PIII 800 runs at 100MHz FSB.
Some of the Taiwanise boards using VIA/SIS/Ali/... chipsets will run the memory at a different speed to the processor, i.e. 100MHz bus/133MHz RAM or 133MHz bus/100MHz RAM.
(2) Intel Celeron
The Celeron only has an FSB of 66MHz, and you can use rock-bottom 66MHz RAM with it. Note, many Taiwanise boards support Celerons running with a 66MHz bus, but with memory at 100MHz or 133MHz.
(3) AMD Athlon (Original/Thunderbird) and AMD Duron
If your motherboard uses the AMD750 chipset, this only supports 100MHz RAM. The VIA KX133 and KT133, the most common chipsets for AMD Athlons, support 100MHz <i>and</i> 133MHz RAM, with a definite performance increase when using 133MHz RAM.
The AMD760 chipset supports 100MHz and 133MHz RAM, plus 200MHz (PC1600) and 266MHz (PC2100) DDR (double-data-rate) SDRAM, but these boards are uncommon at the moment.
(4) AMD K6-2, K6-III
These run at 100MHz FSB and will probably need 133MHz RAM. Some boards allow use of slower 66MHz RAM or faster 133MHz RAM.
(5) Pentium 4
These need a special type of very expensive RAM called RDRAM or RAMBUS. Older PIIIs on an 820 board without the MTH (so just 820, not 820MTH) also need RAMBUS. Avoid it at all costs