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They both allow multiple physical devices to operate as one logical device. VSS only supports "pairs" while stackable switches support multiple units; currently, I believe all now support up to 9 units (as also mentioned by Leo). The stackable switches generally use special modules and cables, and need to be very close together, physically. VSS uses "ordinary" Ethernet connections, and can be spread miles and miles apart (although they are usually near each other).
There are subtle differences in how they actually operate. For example, VSS may try to avoid using the links that connect the pair while stacked switches don't avoid using their stack connection.
Hardware and software requirements vary. For example, in the 6500 series, only certain sups support VSS, and when running in VSS mode, only certain line cards are supported. On the 3750s, stack ports and cables are "standard" but on the 2960S stackables, special modules need to be added.
