in my opinion (mostly in reply to the OP and compozine):
1.) we all here are educated people with some level of privilege by the sheer fact that a.) we're hanging out on the internet/have computers/have internet access and b.) that we're all able to handle the time, cost, etc. of applying to med school. to me, this means we, by taking education and accepting privilege, have entered into a contract with society that we will give to it as much as we can. i think volunteerism is the responsibility of all people with the ability to do so. but then, my volunteer work led me to want to change careers to medicine, medicine was not my drive to do the volunteering...
2.) there is never, ever, a good excuse for being bored. anyone can learn something from any experience, you just have to try to figure out what that is and, if necessary, make the opportunity within the situation. stuck transporting patients? talk to the patient (if awake), try to assure them (within reason), learn something about them, as the dr/nurse more about their case to get some insight, etc. stuck filling out forms? use it as an opportunity to learn something about billing/medicare/insurance/etc. in nearly every setting most people will be more than happy to teach you if you don't know -- you just have to ask. you have to admit you don't know, and ask, and not expect it to be handed to you. and this both helps you learn something and makes the person you're asking feel good about themselves because they can help you and they can feel like the expert they are.
EDIT: and as for "no one gets to do anything major," not true. you just need to invest time into getting trained to do something "major." sure, you won't be doing open heart surgery, but like i said earlier, get and USE and EMT-B, and the ER at the hospital will give you much more interesting things to do as a volunteer. or invest a few months in getting trained to be a lay healthcare worker for a free clinic, and you'll even be seeing clients on your own, if only for vaccinations or HIV test, but it's all you doing the care...