If you are planning on pursuing MD.PhD then research is very important. While research for MD looks good and shows that you have a curiosity for learning, it is not a requirement, per se. It is important for research heavy schools, though, so you'll want to look at each school and understand what is important to each one. Pubications are a big plus, but also hard to achieve. If you plan on getting involved in research, only do so if you have a true interest in it...not just to gain acceptance to med school. A long term comittment with research is favored over someone who obviously crammed it into one summer or semester just so they could include it in their application.
Many universities(practically all) offer some kind of research positions for their undergrads, but it's not always very hands on. There are also summer programs that can be applied for throughout the country depending on GPA and interest.