UPDATE: April 3, 2015: Arkansas has passed an updated Religious Freedom Restoration Act (RFRA), and Indiana passes an amendment to its RFRA law that has generated so much controversy. I have updated the spreadsheet, and it is changed in the original post, as well as attached to this post.
The law that the Arkansas governor eventually signed is basically a mirror of the federal law. It doesn't mention businesses, and it can only be used in cases involving the government. It also did not add any explicit protection against discrimination.
The changes to Indiana's law are actually quite small. It still allows businesses to claim religious freedom protection, and it still allows individuals to use the law in private disputes. What it does add is a section saying that this act can not be used to discriminate in accommodations, employment, or housing based on race, color, religion, ancestry, age, national origin, disability, sex, sexual orientation, gender identity, or United States military service. But, it includes an exception for churches and church officials. I assume this is to clearly allow churches or religious schools to not hire someone if it offends its religion.
Also, the anti-discrimination protection only applies this this specific law. It does not give broader civil rights protection to people based on sexual orientation. It only says that a person can not use the religious freedom law as a defense. But, since sexual orientation is not protected by any civil rights laws in Indiana, a person would not need to use this law as a defense for discrimination based on sexual orientation.
What this means is that if a gay person is refused service at a business, that business probably never needed to use religious freedom as a defense anyway, because there is no Indiana state law that says they can't discriminate based on sexual orientation. All this new law does is say that a business can not use religion as a reason for discrimination.
But remember, that cities and counties in Indiana could enact anti-discrimination acts that would cover businesses in those places.
The Bottom Line
What should business owners take from all this? Unless you can point to a valid business-reason for hiring, firing, refusing service, or rejecting clients, you should be very careful. Even though there may be no law that will get you, public opinion is often an even more powerful force for businesses.