In fact, both Intel consumer processor brands came to life as the
result of Intel being forced to defend against AMD. The reason
Celeron brand came to life is pretty much described by Tony. And
soon-to-be buried Pentium was ment to be 586 - the natural
continuation of x86 line of CPUs. But Intel problem was that as a
result of lengthy legal battle (OK, only one of many implications
thereof) AMD retained the right to reverse-engineer and produce any
x86 Intel CPU, as long as it is sold not as i486 (for instance) but as
Am486. AMD became quite good at this - their 486DX2-80 were faster
than i486DX2-66 by a good margin and about by the same margin cheaper,
and were drop-in replacements. So Intel didn't want this to repeat
with 586. Therefore, "Pentium" - Greek for "Five" with Latin suffix
added.
That's not 100% accurate. AMD was specifically forbidden from reverse
engineering ANY future Intel CPUs, regardless of what they were
called. They were given the right to continue selling their 486 chips
(though by the time the settlement was finished AMD had completed
their own 486 design). It didn't matter what Intel was going to call
their next generation processor, AMD was definitely NOT going to be
able to copy it. They were granted the right to use the Pentium (but
not PentiumPro) bus, but the processor cores had to be of AMD's own
design.
The 'Pentium' name stemmed from a separate but related arguments in
the courts over trademarks, not patents or reverse engineering or
anything like that. The courts ruled that Intel (or any other
company) could NOT trademark a number. So while they could (and did)
trademark i486, there was no legal means that Intel had to prevent AMD
from selling chips labeled Am486. Words, on the other hand, could be
trademarked, hence the "Pentium" name. No one other than Intel is
allowed to sell a processor with the name "Pentium" or some
sufficiently close derivation of that.
These were only 2 of many Intel moves forced by AMD competition,
including premature birth of Pentium in Socket4 - the first Intel
attempt on space heater,
While the Socket 4 Pentiums weren't exactly great chips, I don't think
AMD did much of anything to rush this. That chip arrived as expected
and more or less on schedule.
Rambus is a whole other deal and didn't really involve AMD all that
much. In fact, if anything it was more VIA that forced Intel to drop
their RDRAM plans, not AMD. AMD's market share grew by 1 or 2
percentage points as a result of the Rambus affair. VIA, on the other
hand, went from something like 10% of the chipset business up to 50%
of the business in about a year.
SSE - belated answer to 3dnow, and so on.
SSE and 3DNow! started out at about the same time and both were kind
of natural extensions to MMX. AMD just happened to reach the finish
line quicker with a much simpler design. Intel's answer, SSE, took
longer and was more complicated, though also slightly more complete
and with more room to grow.