Regardless = without due thought or consideration, without regard to. In spite of = in defiance or contempt of something. There is a subtle difference.

thanks!! and i have a question. could i use "anyways" instead of "regardless" in that sentence?: it was raining outside but we left for the beach anyways.

Gah, I put an answer in the comment bar! oops.

I wouldn't worry too much about the distinction. In the majority of cases, they are equivalent, and used interchangeably. (En la mayoría de casos, son iguales.) In spite of my attempts, I could not think of any significant difference in their usage. :P Regardless sometimes can be used in places where "in spite of" would be awkward or would need an object. Por ejemplo: It was raining outside. Regardless, we left for the beach. (regardless of the rain is implied) vs. In spite of the rain, we left for the beach. (with in spite of, the thing that is being spited must come right after the phrase.) It was raining, but