Under what license can I use /usr/share/dict/words?

First you need to determine what package the files belong to. You can use dpkg -S searchterm for that. For example, dpkg -S /usr/share/dict/american-english yields:

wamerican: /usr/share/dict/american-english

So, the subject package is wamerican. All packages I know of have a copyright file in /usr/share/doc/PACKAGE-NAME/copyright. wamerican is not an exception, it's copyright file is in /usr/share/doc/wamerican/copyright.

http://packages.ubuntu.com/natty/wordlist

Find the license by clicking the specific package and looking at the copyright over on the right.

(Found this by googling /usr/share/dict/words, and the wikipedia page http://en.wikipedia.org/wiki/Words_(Unix) said it was the wordlist package)

For example, the american-huge wordlist copyright is here: http://changelogs.ubuntu.com/changelogs/pool/main/s/scowl/scowl_6-3/wamerican-huge.copyright