One thing that seems certain in any campaign is that the Adventuring party of at least some of its members are going to experience an on-going conflict with someone.  Over the years, I've had PCs get into trouble with members of the nobility (both upright and unscrupulous), local law enforcement, cults and an assortment of guilds, cartels and other organizations (both the legal type and the criminal underground).  
It seems reasonable to me that any of these might well choose to put a price on the head of one or more of the player characters as a result of their actions.  My question is, How can I do this and have it be both fun and fair to the party?
Has anyone else dealt with a situation of this kind?  If so, please share your experiences and advice.

I mean, you could just add a chance for them to encounter bounty hunters as a random encounter, which increases as they draw closer to the place where the bounty was issued. It shouldn't really pose a huge problem anywhere except for where there are posters up calling for their heads.

Make a bounty hunter or another part of adventures, and roll every day to see if they attack / are encountered. 

Basically what TheHumbug said.