depends on tires. some tires have a specific direction that their threads are patterned for.

for example, my Goodyear Eagles have a little arrow on it that tells me which direction the tire should be spinning during normal drive. as such, that only allows me to rotate the tires from front to back, and back to front.

but even if that weren't the case, i would only rotate my front two tires to the back and the front two to the front, without switching sides.

why? because radial tires have steel belts in them. after you have driven them for so many miles, they become shaped a certain way. when you switch the tires from left to right, it's no longer correct. i personally believe that this is bad for the tire, and i've been told by my cousin (former mechanic) as well as my current mechanic and several others to only rotate them the way i've been doing so, and not to criss-cross them.
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Kenric Tam
1990 Volvo 740 base sedan (B230F)
My Volvo 'Project'