Final answer:
The Supreme Court decision that limited the right of non-felony defendants to have court-appointed counsel is Betts v. Brady. However, this decision was later overturned by the landmark case of Gideon v. Wainwright in 1963.
Step-by-step explanation:
The Supreme Court decision that limited the right of non-felony defendants to have court-appointed counsel is Betts v. Brady. In this case, it was ruled that indigent defendants may be denied counsel when prosecuted by a state. However, this decision was later overturned by the landmark case of Gideon v. Wainwright in 1963.