Thanks to a post at OpenSourceCommunity.org, I came across a conversion tool to allow you to import the SMF 1.1 database into a phpBB 3 site. Information about the conversion tool can be found in a forum post at phpbb.com. By the way, the script is still in beta, meaning that it works but you might find some bugs since it is not fully tested.
It is not that I'm encouraging anyone to convert their site from SMF to phpBB, but it is very nice to have options such as these available. In fact if anyone can point me to a good conversion tool for migrating a phpBB database to SMF, I would welcome the information.