At my school, they say that most hospitals will take you in as a CNA once you've finished your first year. Some of the local job openings I've looked up online do say they will accept students currently enrolled in an accredited nursing program in lieu of certification.
I'm still in my first year so I guess I'm not ready for that yet myself. I've heard that you can work for a nursing home as a home health aide, which is like a CNA, without any prior training or certification. I'm worried however that it won't be as valuable as experience in an actual hospital, because I'd like to work in a hospital eventually.
Thanks so much for all the advice, everyone!