An interesting discussion regarding volunteering is buried in the comments here. The question is, if you're just starting out and don't have any internship experience, does volunteer work count? What about unrelated non-office work?
In the environmental biz, internships and OSHA certifications are a big help when you're just starting out. Volunteer work is a little more iffy. I don't think that volunteering for an environmental cause is much of a draw unless you can show significant leadership or a serious time commitment. And if you come in all "Yay! I'm going to save Mother Earth!" it makes me worry that you don't realize the dirty, non-glamorous work that we actually do.
So what sort of non-environmental consulting work experience would I like to see in entry-level folks? For me, office experience is sort of a take it or leave it thing. But one thing that I do like to see is experience in being outside in all sorts of weather, working long hours. Because the number one reason why people bail out of environmental work is the drudgery of fieldwork. Getting rained on. Getting cold. Some people don't last a week. So, landscaping experience is good. Or construction. Or being a former camp counselor. Or farm work.
I do think that folks who want to be more than technicians need to have a strong science background, which means good grades or a good explanation for your grades. And strong communication skills are important if you want to advance. But all that doesn't help if you can't handle the fieldwork.