If you go to http://homepath.com you can search the homes available for HomePath financing. Once the property is out of the "first look" stage, they are available for investors with 10% down, no appraisal and no PMI.
Non existent on the conventional side. There isn't appetite for these loans in the secondary market. I can get you in with 5-10 down with hard money but there has to be potential equity after repairs and it would cost more. . This would be more ideal for buy and flip, not holding. Has to be non owner so you would have to have a designated homestead or close in an LLC.
You will have a tough time finding a lender that will do it. There may be a couple lenders that will do 10% down at a 7 to 8% interest rate but I dont know if it is still available.
If you are looking to do a flip, there are some "hard money" loans that will be 0 down but the balance will be due in 6-12 months max. So you dont want that if you are looking to buy then rent it. Let me know if you want some help with this as I do work with investors often and I am one myself. Thanks!