If my brother dies intestate and has no will and no children, who gets his estate?

Under Florida law, the estate would first pass to his parents (if living).  If neither parent is alive, it would then pass under Florida law to his siblings (brothers and sisters).  If he had no siblings, it would pass to nephews and nieces, etc. Only if he had NO living family members would it pass to the state of Florida (a very rare occurence). 

This plan of descent may not have been his intent and only emphasizes the reason why it is important to have an estate plan in place.

If your parents are no longer living, your brother's estate would go to you and your siblings (if any), in equal shares;  if you had another brother or sister who was deceased but left one or more children, the children would take their parent's share.

You have an "estate plan," whether you have a will drawn up or not.  It's just that the plan you get, if you do nothing, is the one-size-fits-all intestate succession statute.  If you care what happens to your money and property after you're gone, you need to understand how that law works, in your case, and then you need to decide if you're okay with that or not.