OK, I found out why. It turns out that JSTL is not part of JBoss/Tomcat (gasp). Refer to here: http://www.jboss.org/index.html?module=bb&op=viewtopic&p=3856268#3856268
As was posted there, I copied standard.jar and jstl.jar from Sun's J2EE tutorial to my /WEB-INF/lib/ directory and reployed. Now it works. I'm not sure where else to get them or whether there're more "official" versions than in the tutorial.
So the "Standard Tag Library" is not part of the standard. Interesting.