With most of my transactions, we assume that the title is clear or that it will be cleared by the seller prior to closing. It is very unusual in my area of operations to encounter issues with the title that make the deal impossible to put together.
However, there are occasionally issues that do persist, and come back to haunt you years later, which is why I generally recommend that my buyers purchase an owner's title insurance policy. When that sort of a policy is issued, the insurance company that writes it is saying that they have inspected the title and found it to be clean, but if at any point during the time that you own the property, you find that there are issues with the title, the title insurance company will correct those issues, at their expense.
So, in summary, issues are rare, but when issues do arise, they either do so prior to closing, or if they appear after closing, are covered by an owner's title insurance policy.