Yes, if you are using SSL sitewide, then I definitely recommend enabling HSTS.
HSTS is an important security measure to defeat man-in-the-middle attacks that shift the user over to http and then attack the user. For instance, sslstrip is a well-known tool to mount such an attack. For more details on this sort of attack, see the following questions:
How to thwart sslstrip attack?,
Options when defending against SSLstrip?,
and this answer.
HSTS tells the browser: never use HTTP with this site. Only access it via HTTPS. So, to enable HSTS, you must make sure that your site works with HTTPS, and only HTTPS. This includes everything: HTML, CSS, Javascript, everything. Make sure all of the CSS and Javascript on your site is available over HTTPS. Also, I suggest that you convert your pages to reference everything over HTTPS (I recommend your pages avoid loading any other Javascript or CSS resource over HTTP, as that may cause warnings or security problems for some browsers).
For instance, let's say your site is www.example.com and you have a page https://www.example.com/buy.html which includes some Javascript from your site. You must make sure you your Javascript file is available on a HTTPS URL (e.g., https://www.example.com/library.js). I recommend that you load it via a HTTPS URL (e.g., <SCRIPT SRC="https://www.example.com/library.js">).
P.S. I also recommend that you set the secure flag on all cookies you use.