I'm not sure which side I come down on, there are lots of factors to take into consideration.
Since everyone seems to think the that it should remain illegal, I'm going to make the argument that it should be made LEGAL.
Free-market principle: adults with free wills should be able to make decisions as to which economic activities they want to engage in, as long as it does not do harm to other people. This assumes that the harm that it would do to "public morality" or "people's sense of decency" doesn't hold any ground, or that the harm to prostitutes (or people who become infected with sexually transmitted diseases) that results from it being illegal, grossly outweighs any harm to public morality.
If a woman owns her own body, the state should not violate her right to do whichever she pleases, as long as she is not harming other people in the process.
If prostitution were made legal, the business would be taken out of the hands of criminals, who might use the ill-gotten gains to further other criminal ends. It would also be a blow to any criminal organizations such as gangs or mafias that may control prostitution.
It would cut-down on the victimization of prostitutes because they wouldn't be taken advantage of by pimps. There would be no such thing as women being in prostitution against their will, because if the government was in charge of it, women could enter and leave the profession freely as they chose. No one could force them to stay in prostitution.
The proliferation of sexually transmitted diseases would be lowered because the government would regulate prostitutes and they would be checked for STDs and there would be specific regulations as to condom use, etc. that would cut down on the spread of sexually transmitted diseases. There would be little chance for the prostitutes to be abused, because if they were abused, their abuser would be able to be charged by the state. Currently, prostitutes fear going to the authorities about abuse because they are afraid that they will be arrested for doing so, so they are allowed to be abused with impunity.
Of course these arguments only work if the rates of the government regulated prostitutes would be the same as the illicit prostitution current-market rates or lower.
In summation, the spread of STDs, abuse of prostitutes with impunity, and the coercive ability of pimps to force their prostitutes to remain in the business would all be nearly eliminated.
Have you guys ever seen the reality show of the prostitutes in a Nevada brothel? They are well taken care of, they get paid well, they are not infested with diseases because they are regulated, and they are able to leave prostitution freely as they choose. I remember there was one lady who was getting paid well enough where she was going to leave prostitution and start her own business. Now compare that to the common street prostitute who is at the mercy of her pimp, is completely unregulated as to STDs, and who is sometimes forced at threat of herself or family members to stay in the prostitution business.