I think John's answers are great. Teaching assistant and/or research assistant is a great way to volunteer and get to know some interesting people that could help you later in your career (i.e., the professors). Finding an organization to volunteer with for a summer or other semester would also be great (as John also suggested). Working as a referee/official is a great experience, you could also consider coaching youth sports (great way to learn some life skills and meet parents who may be able to help you get a job later).
If you're looking to volunteer I think there are MANY options and I'd encourage you, like John did, to start with what your school offers and then branch out. There are also a variety of online websites dedicated to compiling volunteer opportunities. But, I would recommend determining what you are interested in (not necessarily passionate about, just interested in) and going from there. My suggestion would be to consider starting with short investments of your time to get a sense of how volunteering makes you feel (for example, you could volunteer at a local charity event, or show up for a trash pick up day, etc.). You may also want to investigate businesses around you and see what sparks some level of interest and reach out to them about the potential to volunteer or even shadow their operations. Lastly, you may also want to seek to participate in some on or off campus clubs/groups related to interests of yours (for example, local rotary/community service clubs, entrepreneurship, environmentalism, athletics, etc.).
To directly answer your question though, when I was in college I wasn't able to volunteer much. I was a student athlete and worked part time to help pay for my schooling. During the school year I worked at the on-campus memorial union (i.e., where students went to eat during break) serving food, and during the summers I coached (sometimes as a volunteer) and lifeguarded. I worked an internship at the end of my college career with a local professional sports team and learned a lot.