2010 Frigidaire:
Normal, Whitest Whites, Heavy Duty, Bulky, and Sanitize Cycles: Wash, spin, rinse, spin, rinse, final spin. If you choose "Freshwater Rinse" (their term for an extra rinse) the sequence is: Wash, spin, rinse, spin, rinse, spin, rinse, final spin.
Casual (permanent press) Cycle: Wash, rinse, spin, rinse, final spin.
Delicate: Slow tumble wash, rinse, rinse, final spin.
Personally, I like a spin after the wash and each rinse, with the exception of the Casual cycle, which provides a cool-down via the first rinse before there's a spin to set wrinkles in dress shirts.