It depends! You should have excellent credit and money management skills.

Because if you can't handle money now, you will fail at homeownership.

I saw a program last night (3 am) revealing how I can buy and sell real estate and use none of my own money. 
Your question implies you are seeking a mortgage to make a resideintial property purchase. Every lender has their own critera and ratios to which they must adhere. At the start of the Chase cycle a 700 score will get you money but at the end of the cycle, when the ratios are met a 740 gets the money.
When scores are below 700, you really, really, really need to touch base with a mortgage broker (not a bank) to find who is willing to get you into a house. A LOCAL broker may also know of other resources available to  reduce cost or even price that should be beneficial to a buyer.
I don't want to sound self-serving, but it may be a good action to contact a REALTOR who sign appears in the yard of properties you like, so they can help you identify a lender who knows how the get the job done.

Zero, if you have enough cash.  Do you want to know what the minimum credit score one can have and still get a loan from a bank? That's a different question.

I am not a lender, but I think it is at least 620.  I know lenders can also do it with lower scores, but the terms are different and there are a lot of other factors that go into it.  The higher the score, the better the rate!

720+ for the best rate

Your local lender would be most helpful to you

Great answers here, Daniel. It is easy to say, the higher the better. Don't forget, you also need ability to repay...general, a job. Also, you will probably need at least a small down payment unless you qualify for certain specialty loans like VA.

I suggest you work with a great local lender and allow that person to guide you on lending criteria.  

I've heard from lenders who can 'manage' to work with numbers as low as in the high 500's, but that can be a very difficult loan.

These days, lenders consider the low to mid 700's a "good" credit score.  Even scores in the high 600's can make them smile.

the higher your score the easier it is to get a good interest rate... those lower numbers will cost you a premium.

In general, 640. The higher your score, the better your rate/fees. There are lenders that will do FHA loans down to 580 but you will pay a higher price for those loans and you need to pretty much be paid as agreed for the last year on all your credit.

Lots of different programs but I've heard like 550 the lowest. That's some messed up credit with that number.

Here today just in time for you is the answer from GENE MUNDT, IL/WI MORTGAGE ORIGINATOR - FHA/VA/CONV/JUMBO/PORTFOLIO/REFI

See esp. end of article on credit scores.

https://activerain.com/blogsview/5537131/i-need-a-mortgage--what-interest-rate-can-i-get-

Gene Mundt, IL/WI Mortgage Originator - FHA/VA/Conv/Jumbo/Portfolio/Refi  just posted a great article on AR about rates and the process of obtaining a loan approval.  I highly recommend reading that to get a more indepth perspective.

Yes, right, DEPENDS, as Candice A. Donofrio said.

Jason E. Gordon 

Just wrote a post regarding this very topic, Daniel Elton ... here's the post/link: 

What Interest Rate Can I Get on a Mortgage?

If you have questions or are in need of clarification, give me a shout ...

Gene

Depends upon the mortgage loan.   720+ is ideal.  Mid 600's will start a conversation with many lenders.  High 500's maybe you can get a high-risk FHA loan. 

BTW, the score that you get from Transunion, Equifax, Experian (Free Annual Credit Report) may NOT be the score that your lender sees.  

As others said, talk with a lender.  I suggest that you start at your own bank or credit union (if they offer mortgage loans).

Different programs have different minimum credit score requirements. We also look at the loan amount, purchase price, and your cash-flow (amongst other things) when evaluating a Borrower's ability to meet approval guidelines. Feel free to reach out to me directly if you wish. My direct line is 619-200-8031, email is jgordon@amerifirst.us

You should contact a good lender to find out all of the programs available.  There are many options that affect needed credit score including paying all cash.