There are a lot of ways to milk BYU for all they will give you.
BYU students are entitled to 1 free bowling game per semester. You might have to go on weekdays before like 6 though.
International Cinema - Free movies in the SWKT. Other departments and clubs also have film series from time to time.
Free food at club events, as well as department events and promotions, etc.
Free counseling, therapy.
Women's Services offers classes for people with eating disorders, relationship issues, and what have you. Apparently they also give out free tampons if you ask.
Free tutoring! Also, if you happen to have a disability you can get people to help you take notes in your classes.
Use the library, it is one of the best college libraries in the country. You can check out some movies for 3 days, and you can also rent music. You can watch other movies in the Learning Resource Center. You can get help with your research papers from the librarians.
Classes at the Career and Counseling Center. There are classes on budgeting, speed reading, time management, and other things.
Go to lectures every day. Since you are paying to attend school, skipping class means you are not getting something you paid for. There are also additional lectures like devotionals and forums and also the ones hosted by the Kennedy Center. Sometimes they have ambassadors and other really awesome people come through.
Use office hours from both your TAs and your Professors. Not only will it help you get better grades, getting to know your professors can help in terms of getting research jobs and letters of recommendation. BYU has a lot of research and TA positions available for undergraduates.
Use the recreation facilities. The gym, pool, etc. The hours, especially for the pool, may not be that ideal but yeah it's free for students. You can also join intramural teams..
Go to the Museum of Art, the student art shows in the HFAC. They're usually free. Also go to student productions like choir and orchestra performances. Usually you can get a student discount and they're all really talented.
During finals week there is a lot of free food, like pancake breakfasts at the dorms and stuff.
BYUSA gives away free t-shirts to help advertise for their events. Also, BYUSA sometimes will have free food at random times to try and get people to give comments or vote or whatever.
Free concerts during lunch on Fridays, and Guitar Explosion about once a month in the evening.
Free computer classes, hosted by the library.
Free math tutoring at the math lab. Also there is a free writing lab in the JFSB, to help you edit your papers.
Discounts on computer stuff. If you might ever want to use Adobe Creative Suite you should buy it when you're still a student, there is a huge discount for that. Apparently you can also get a discount for a friend but you can only do that once a semester or something.