I guess it would depend on why they turned the offer down.  If it was due to some type or personal issue, I would consider them in the future.  If it was due to salary and we could not come to am agreement, I would not consider them for future positions unless they reapplied. 

Sheryl

I see this as an opportunity to build bridges. I would remind them that you thought highly of their candidacy and you're sorry they're not joining your team. I'd ask for a favor - What was it about us/our offer/the job that you didn't like? (Their answers may be helpful in a number of ways!) I would invite them to stay in touch and connect on LinkedIn. I would consider them for future roles (depending on why they said no to the initial offer). And, I would ask them if they know anyone who might have an interest in the job they declined. I would also offer to return the favor if I could help them network in any way in the future.  Hope this helps!

I would agree with everything both Sheryl & Chucked had to share. I've found through years of recruiting that I there are some many factors that play into the offer being accepted or declined. I'm going to want to stay connected and consider the applicant in the future unless it just doesn't seem to make sense why they are declining. 

For instance, if I as the recruiter have given the applicant everything they were wanting such as a better opportunity, a step up in their career, increase salary, smaller commute, etc. and they give me a vague answer as to why they are declining I may really have to think long and hard about future opportunities.