Universal College Credit Act - Amends the Internal Revenue Code to allow a tax credit up to $4,000 annually for the qualified tuition and related expenses of an individual taxpayer, a taxpayer's spouse, and dependents. Allows such credit for four years of undergraduate education expenses and six years of graduate or professional education expenses. Excludes expenses for courses involving sports, games, or hobbies (unless part of a degree program) and expenses unrelated to an academic program (e.g., student activity fees, athletic fees, or insurance fees).