Actually Intel HAS had a few problems in the past, though generally not as many as its competitors.
Take the MTH issue with the I820 boards for example. This "memory translator hub" was supposed to allow people to use either RDRAM or SDRAM on the motherboard, however the board would only function with RDRAM without a fatal result. Many chipsets were shipped back to Taiwan after angry customers brought them back to the store.
Also, there were some actual bugs with Rambus and Intel's first Willamette 423 pin processors when the very first ones were released (just the brand new ones though, this was resolved shortly).
Mainly though, with Intel you'll experience less compatibility/stability issues, however you'll have poorer performance compared to systems with AMD processors.
But Intel made some bad decisions even if they didn't result in stability issues when they first started working on Pentium 4 technology.
They had this "4x quad pumped" idea, Rambus was way too expensive at that time, also it didn't perform all that well, there was PC600 and 700 along with 800, not just PC800 at that point in time; and the latency times weren't optimized. The first P4 processor itself didn't perform that well either, the pipelines were too small, and P3's actually beat them at certain applications.
To be honest, if you get an AMD processor and go with an SiS 745 chipset, I don't think you'll have any problems. SiS was even considerate to post a memory validation chart on its webstie.
Beyond that, chipset wise, I wouldn't deal with VIA as they have a ton of compatibility and stability problems. To this day they are still talking about revising already made chipsets like the KT400B now.
That leaves you with ALi, which I wouldn't bother with. ATi has made a few chipsets, but I wouldn't mess with those either.
You could go with an AMD chipset, I think they are making an Irongate 761 now, this will probably not have any compatiblity issues, I would assume one who knows how to make processors could make a motherboard chipset most compatible with them and other components. Though an AMD motherboard probably won't offer the best performance.
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Benchmarks don't lie