Really, your career depends on what you want to do with it. If you find that research just doesn't thrill you the way other activities do (like interacting with patients or learning about music theory), then don't force yourself to do it! It isn't worth your time if you won't gain something valuable from the experience.
In terms of applying to medical schools, as long as you show you have an interest in serving others (through community service/volunteer work or community activism, by shadowing physicians, etc etc etc), I think you will be fine. (Of course you should also try your best in your courses and on the MCAT, too).
(people, correct me if I am wrong with anything below🙂
There are some very research-oriented medical schools that tend to have their graduates go into academic medicine. Sometimes, their curriculum will mold students into having the skills of a physician-scientist (even if you don't go for that MD/PhD part) by requiring a "research/scholarly project." Now, this might vary depending on the school, because the project could be purely clinical or basic science research at one school, but at another school, it could be a paper on absolutely anything related to medicine, like bioethics or healthcare economics. Some might require the paper to be published, others might just require a graduate-level write-up...basically a thesis, anyway. I feel like those medical schools that train their students to think like a physician-scientist might value applicants with research experience more, but I do not know how exactly this affects admission into their programs. (Maybe someone can also comment on this?)
But then if you look at the whole of medical schools, many will train you to be a good practicing doctor, and thus, what they are looking for in their applicants is not purely research experience, but valuable, unique experiences that demonstrate maturity. Basically, prove it to the admissions committees that you are a lifelong learner, independent thinker, good team-player, who is empathic, personable, and dedicated. You can do all that without research.
I seriously would not worry about not having enough research experience. If you are, however, did you just try basic science research and not like it? Maybe you could look into getting some experience in clinical research. You'll have plenty of opportunity to work with patients, instead of working with post-docs and eppendorf tubes like in basic science.
(Don't get me wrong, I love research!)