FHA mortgages require a 500 credit score, and most FHA lenders minimum score requirements tend to be 600, 620, or 640 - with FHA anything less than a 580 score requires a 10% down payment, otherwise just 3.5% down is required.
VA mortgages have no score requirement, but VA lenders score requirements are similar to FHA's. VA is 100% financing for Veteran's.
USDA Rural Development mortgages have no score requirement - however if you go through a lender most will have 620 or 640 minimum scores, but if you go *Direct* to USDA they do not have any minimum score requirements, but it takes a little bit longer - Harrah is an eligible area, all the way west until Chocotaw Rd.
http://eligibility.sc.egov.usda.gov/eligibility/welcomeAction.do to check the eligible areas and also if your income is not too high/within eligibility limits as well.
Fannie Mae & Freddie Mac mortgage programs require a 620 score, however with less than 20% down you will likely need at least 660-680 scores.
Credit score isn't the only item considered though, what is on your credit report is equally as important. If there are late payments or delinquent accounts in the last 12 months when you apply then that can curtail your chances of qualifying. If it's free of those items for the past 12 months then your credit may be good enough as it is. If there is good reason for negatives, such as an accident at work that prevents you from making money, a medical situation keeping you from working, or a death of a family member who was a wage-earner (among other situations) then that is taken into consideration.
Feel free to ask more questions or provide more information about your situation to get further evaluation.