Final answer:
The Supreme Court case 'Citizens United v. Federal Election Commission' ruled that corporate spending limits imposed by BCRA violated the First Amendment, leading to corporations having the ability to spend unlimited money on elections without disclosing donors.
Step-by-step explanation:
The U.S. Supreme Court case that created the opportunity for those opposed to powerful incumbents to create organizations without having to disclose their donors is Citizens United v. Federal Election Commission, 558 U.S. 310 (2010). This landmark decision, made by the Court in a 5-4 ruling, argued that the restrictions imposed by the Bipartisan Campaign Reform Act (BCRA) on corporate spending in elections violated the First Amendment right to free expression. Consequently, this decision allowed corporations and unions to spend unlimited amounts of money on political elections, and led to the formation of super PACs that can raise unlimited funds without disclosing their donors, provided they do not directly coordinate with candidates' campaigns.