Can a retiree with free time on his/her hands sit in on college lectures and learn the material for free or are there rules against that? Naturally they wouldn’t get a grade and may not be allowed to take tests but what about just sitting in on the lecture and learning the material, is that allowed or are you required to pay for that?
You ask the professor nicely on the first day of class and be very polite. Since you’re not getting credits, and they’re just happy to be sharing what they know, they’re usually cool about it. Defer to the people who are paying, as far as time consumption goes. Most schools are, at least unofficially, pretty cool about it as long as you are cool about it.
It depends on the school:
School of Education, Bloomington, 2003
As capybara says, some profs will just let you sit in on the course for free.
Some schools don’t like that, and some classes like freshman calc, or physics are so large that no one will ever notice you sitting there.
Call the school your interested in and ask them what their policy is.
My university had a special registration form for over-60 auditors, who were allowed to audit classes free.
Many colleges have a policy of allowing seniors to audit classes for free. Contact your local college to see.
In Hawaii you can!! 
The Senior Citizen Visitor Program (SCVP), administered by Student Equity, Excellence, and Diversity (SEED), is available to residents of Hawai‘i who are age 60 years and older. The program allows senior citizens to participate in University of Hawaii at Manoa classes offered during the fall and spring semesters, provided they have the consent of the instructor. Participation in SCVP entitles the visitor to use libraries and other UH facilities. Visitors are exempt from tuition; course credit is not awarded, and permanent records are not maintained. Senior citizens wishing to receive credit for courses must apply for admission to the UH and must pay all tuition and fees.
Auditing classes is very common - as long as auditors do not displace regular students.
In my experience, most professors don’t mind at all if a non-paying student sits in on a class. Any decent teacher loves teaching, and loves having students who want to learn. Also in my experience, the administration of the school generally frowns on this practice, since they would much prefer to charge for auditing. Yet again in my experience, though, the administration almost never finds out, unless the student is fool enough to tell them.
I’ve sat in on several classes which I was interesting in but not interested enough to actually take the class. I never bothered about asking the lecturer. Classes never filled over 1/2 a lecture hall so there was no way of me crowding another student out and it’s not like they had to expend any more effort to lecture to one more person.
Every uni lecture I’ve ever been to has enough students that the lecturer would never know who was auditing and who wasn’t.
As a young student, I would sometime crash lectures that interested me, and I saw a lot of interesting lectures that way. No problem.
Senior auditors are also generally welcome in class - provided they don’t monopolize the discussion with their Grandpa-Simpson tales of travel, world events they remember, what they read in some article once, etc.
Well darn, my introduction to the class was going to be on liberty cabbage and the war.
Of course, sitting in on a lecture isn’t the same as auditing a course, which assumes you’ll attend regularly. Sitting in on an occasional lecture is IME encouraged by school administration as a way of allowing students to see what other areas they may be interested in as well as giving visitors and prospects something interesting to do when they visit campus.
–Cliffy