I also know that you can order vital records online, for a fee, from 1921 on.
The question this left me with is: how/where can one access records from 1916-1920?
I recently discovered that you can find them-- if you already know the date of the event-- on FamilySearch.org. Yep, I've been going to this site for over a year, and just now discovered this.
The thing is, the records aren't archived, so you're not going to find them by doing a basic name/date search. And you will have to already know the place and date of the event; I'm going to find the death record of my great-great grandfather Thomas RYAN, who passed on 9 August 1916.
1. You first go to FamilySearch.org's home page, and then scroll down to the "Browse by location" links. Click on "United States", then "Massachusetts."
2. Click on "Massachusetts" from the list of states. Then choose the last listed database, titled "Massachusetts State Vital Records, 1841-1920."
3. Click on "Browse through images." Select from births, deaths, or marriages. Here, I'm looking for a death, so that's what I'll click on.
4. Thomas died in Boston, so using the scroll bar on the right (easy to not notice it), I'll scroll down till I come to "Deaths 1916" for Boston-- here are two volumes. By digging around, I realized that they were in chronological order, by day, for the most part, so I had to do some searching to get to August.
5. Voila, I found Thomas's death record on page 152 of the second volume of 1916 deaths for Boston, and saved it to my puter.
Discovered much from this record: his exact birthdate (25 July 1831), his parents' names, including his mother's maiden name (I could now change "Johanna Unknown" in my tree to "Johanna LYNCH"), and his cause of death: myocarditis and mitral regurgitation (5+ years), and secondary cause/contributing factor was heat exhaustion (2 days).