In the United States prostitution is almost entirely illegal, with the non Las Vegas part of Nevada the well known exception. Why not in "What happens in Vegas stays in Vegas"? You got me. In any event, we do have this isolated example of legalized prostitution in our country. It is legal in other countries such as Switzerland, New Zealand, the Netherlands, part of Germany and Austria, and, according to the Wiki, it is technically legal in the United Kingom - although associated activities like pimping are not.
Pros and Cons - in a nutshell
On the side of legalization is that prostitution is a consenting choice between adults, that if decriminalized and regulated it would be safer for all involved through the monitoring of worker's health, and would lessen involvement of other criminal groups, that making the act itself illegal is enforcing (conservative) morality in criminal code.
On the side of keeping it criminal is that prostitution encourages violence against women, encourages sex slave trafficking, and encourages further involvement the criminal element if it is legalized. In essence, that it is not a consenting agreement, but in most cases some sort of illegal activity driving the prostitute's choice to engage in this activity. Pro-criminalization advocates also argue that it exploits (mostly) women who use it as a last resort for money and generally objectifies women.