It all comes down to voltage.
PCI-X slots are always 3.3V.
In principle PCI slots can be either 3.3V or 5V depending on which version of the PCI standard they are designed to but in practice 3.3V ones are extremely rare.
Cards can be either 3.3V only, 5V only or universal voltage. Cards and slots are keyed to indicate the voltage.
So if your PCI-x card is keyed for universal voltage then it should work in a regular 5V PCI slot. If it doesn't support 5V then it shouldn't fit in a regular 5V PCI slot. If it fits but doesn't work then someone is failing to follow the specs.
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Maybe this new question adds some interesting detail to the things? http://superuser.com/questions/839893/i-have-a-3-3volt-pci-ethernet-card-working-on-a-5volt-pci-slot-how-is-it-possib
– Sopalajo de Arrierez – 2014-11-14T02:59:17.767This answer is wrong, PCI 2.0 added the 3.3V option but it didn't remove the 5V option. The 5V option wasn't removed until 3.0 and even then there is nothing forcing motherboard manufactureres to use the latest version of the spec. – plugwash – 2017-06-07T14:31:15.980
Thank you! This helps a lot. Since PCI 2.0 was released in 1993, this pretty much means any PCI slot. – Eli – 2011-08-12T20:15:22.923
Just for future reference, the card in question was a Broadcom BCM5701, and it works in a normal pci slot as well as pci-x – Eli – 2011-08-13T00:23:24.903