You need to contact the bar in the state you want to practice and see if they have any reciprocity agreements between the states. For example, if you take and pass teh NY bar, you need to contact the Florida State bar to see if they have a reciprocity agreement with NY bar.
I believe in California, it doesn't matter what state you passed the bar in, there is no reciprocity so you have to take the California bar no matter what.
Generally speaking, you probably would. I believem most big states like California, Florida, Texas, etc. has no reciprocity agreements and you have to take their bar and smaller states like Ohio and Illinois have limited reciprocity agreements.